Average Error: 13.9 → 0.5
Time: 28.6s
Precision: 64
Internal Precision: 384
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.0136371847332 \cdot 10^{+156}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\frac{y}{z} \le -9.068989931951784 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;\frac{y}{z} \le 6.539325462591832 \cdot 10^{-226}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\frac{y}{z} \le 1.3280134257689862 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \end{array}\]

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) < -1.0136371847332e+156 or -9.068989931951784e-289 < (/ y z) < 6.539325462591832e-226

    1. Initial program 22.3

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

    2. Applied simplify15.2

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

    4. Applied associate-*r/0.8

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

    if -1.0136371847332e+156 < (/ y z) < -9.068989931951784e-289 or 6.539325462591832e-226 < (/ y z) < 1.3280134257689862e+176

    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 1.3280134257689862e+176 < (/ y z)

    1. Initial program 35.8

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

    2. Applied simplify19.3

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

    4. Applied div-inv19.4

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)}\]

    5. Applied associate-*r*1.6

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
  3. Recombined 3 regimes into one program.

Runtime

Time bar (total: 28.6s)Debug logProfile

herbie shell --seed '#(1070355188 2193211668 3977393919 3454156579 3755371326 1656365382)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))