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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{z}{x} \le -3.2845100879270977 \cdot 10^{+275}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{if}\;\frac{z}{x} \le -3.933914952147978 \cdot 10^{-304}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{if}\;\frac{z}{x} \le 2.3540314842465144 \cdot 10^{-303}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{if}\;\frac{z}{x} \le 2.3930233669727197 \cdot 10^{+230}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

Split input into 3 regimes
if (/ z x) < -3.2845100879270977e+275 or 2.3930233669727197e+230 < (/ z x)
1. Initial program 3.5
  \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
2. Applied simplify12.8
  \[\leadsto \color{blue}{y \cdot \frac{x}{z}}\]
3. Using strategy rm
4. Applied associate-*r/0.2
  \[\leadsto \color{blue}{\frac{y \cdot x}{z}}\]
if -3.2845100879270977e+275 < (/ z x) < -3.933914952147978e-304 or 2.3540314842465144e-303 < (/ z x) < 2.3930233669727197e+230
1. Initial program 18.1
  \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
2. Applied simplify0.2
  \[\leadsto \color{blue}{y \cdot \frac{x}{z}}\]
3. Using strategy rm
4. Applied associate-*r/8.0
  \[\leadsto \color{blue}{\frac{y \cdot x}{z}}\]
5. Using strategy rm
6. Applied associate-/l*0.2
  \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}}\]
if -3.933914952147978e-304 < (/ z x) < 2.3540314842465144e-303
1. Initial program 7.0
  \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
Recombined 3 regimes into one program.

Runtime

herbie shell --seed 2018296 +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)))

Error

Try it out

Derivation

`if (/ z x) < -3.2845100879270977e+275 or 2.3930233669727197e+230 < (/ z x)`

`if -3.2845100879270977e+275 < (/ z x) < -3.933914952147978e-304 or 2.3540314842465144e-303 < (/ z x) < 2.3930233669727197e+230`

`if -3.933914952147978e-304 < (/ z x) < 2.3540314842465144e-303`

Runtime

In
Out