Average Error: 14.1 → 2.9
Time: 5.5s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.3638961499349904 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.0660667088346729 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if (/ y z) < -2.3638961499349904e-196 or 1.0660667088346729e-284 < (/ y z)

    1. Initial program 12.7

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

    2. Initial simplification7.7

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

    3. Taylor expanded around 0 7.4

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

    5. Applied associate-/l*3.7

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

    if -2.3638961499349904e-196 < (/ y z) < 1.0660667088346729e-284

    1. Initial program 18.4

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

    2. Initial simplification0.4

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

  4. Final simplification2.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.3638961499349904 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.0660667088346729 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Runtime

Time bar (total: 5.5s)Debug logProfile

herbie shell --seed 2018235 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))