Average Error: 14.2 → 0.7
Time: 22.7s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot x \le -3.9632570729893533 \cdot 10^{+295}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \cdot x \le -2.3421821286895737 \cdot 10^{-141}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \cdot x \le 8.507385469605398 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \cdot x \le 8.854482967741617 \cdot 10^{+153}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

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 2 regimes

  2. if (* y x) < -3.9632570729893533e+295 or -2.3421821286895737e-141 < (* y x) < 8.507385469605398e-166 or 8.854482967741617e+153 < (* y x)

    1. Initial program 7.7

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

    2. Initial simplification1.3

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

    if -3.9632570729893533e+295 < (* y x) < -2.3421821286895737e-141 or 8.507385469605398e-166 < (* y x) < 8.854482967741617e+153

    1. Initial program 19.5

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

    2. Initial simplification10.5

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

    4. Applied associate-*r/0.2

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \le -3.9632570729893533 \cdot 10^{+295}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \cdot x \le -2.3421821286895737 \cdot 10^{-141}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \cdot x \le 8.507385469605398 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \cdot x \le 8.854482967741617 \cdot 10^{+153}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Runtime

Time bar (total: 22.7s)Debug logProfile

herbie shell --seed 2018216 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))