Average Error: 13.9 → 0.8
Time: 30.4s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.7265094403537214 \cdot 10^{+144}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\frac{y}{z} \le -2.6288018572505108 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;\frac{y}{z} \le 2.8784423652490492 \cdot 10^{-211}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\frac{y}{z} \le 4.2827272105516214 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

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 z) < -3.7265094403537214e+144 or -2.6288018572505108e-251 < (/ y z) < 2.8784423652490492e-211 or 4.2827272105516214e+128 < (/ y z)

    1. Initial program 23.6

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

    2. Applied simplify13.9

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

    4. Applied associate-*r/1.6

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

    if -3.7265094403537214e+144 < (/ y z) < -2.6288018572505108e-251 or 2.8784423652490492e-211 < (/ y z) < 4.2827272105516214e+128

    1. Initial program 6.7

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

    2. Applied simplify0.2

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

Runtime

Time bar (total: 30.4s)Debug logProfile

herbie shell --seed 2018214 +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)))