Average Error: 15.0 → 0.7
Time: 14.1s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -4.829040713266421 \cdot 10^{+298}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.5680963907121065 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 4.3324850419011754 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 7.58515535781874 \cdot 10^{+214}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \end{array}\]

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 4 regimes

  2. if (/ y z) < -4.829040713266421e+298

    1. Initial program 58.1

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

    2. Initial simplification0.3

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

    4. Applied div-inv0.4

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

    5. Applied associate-*r*0.3

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

    if -4.829040713266421e+298 < (/ y z) < -1.5680963907121065e-99 or 4.3324850419011754e-234 < (/ y z) < 7.58515535781874e+214

    1. Initial program 9.3

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

    2. Initial simplification9.4

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

    3. Taylor expanded around inf 9.3

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

    5. Applied associate-/l*0.2

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

    if -1.5680963907121065e-99 < (/ y z) < 4.3324850419011754e-234

    1. Initial program 16.8

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

    2. Initial simplification1.3

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

    if 7.58515535781874e+214 < (/ y z)

    1. Initial program 42.3

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

    2. Initial simplification1.0

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

    3. Taylor expanded around inf 1.6

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

    5. Applied clear-num1.7

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -4.829040713266421 \cdot 10^{+298}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.5680963907121065 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 4.3324850419011754 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 7.58515535781874 \cdot 10^{+214}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \end{array}\]

Runtime

Time bar (total: 14.1s)Debug logProfile

herbie shell --seed 2018225 +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)))