Average Error: 14.0 → 3.4
Time: 13.2s
Precision: 64
Internal Precision: 128
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le 0.0:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.981763070192266 \cdot 10^{+280}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

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 3 regimes

  2. if (/ y z) < 0.0

    1. Initial program 14.8

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

    2. Initial simplification5.1

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

    3. Taylor expanded around inf 5.4

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

    if 0.0 < (/ y z) < 2.981763070192266e+280

    1. Initial program 9.6

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

    2. Initial simplification7.4

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

    3. Taylor expanded around inf 7.4

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

    5. Applied associate-/l*0.7

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

    if 2.981763070192266e+280 < (/ y z)

    1. Initial program 54.0

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

    2. Initial simplification0.2

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

  4. Final simplification3.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le 0.0:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.981763070192266 \cdot 10^{+280}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Runtime

Time bar (total: 13.2s)Debug logProfile

herbie shell --seed 2018348 +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)))