Average Error: 14.4 → 0.4
Time: 13.3s
Precision: 64
Internal Precision: 384
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\sqrt[3]{\frac{z}{y}} = -\infty:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;\sqrt[3]{\frac{z}{y}} \le -4.353809244386929 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\sqrt[3]{\frac{z}{y}} \le 2.598400643880996 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;\sqrt[3]{\frac{z}{y}} \le 5.1343243090214894 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Split input into 2 regimes

  2. if (cbrt (/ z y)) or -4.353809244386929e-70 < (cbrt (/ z y)) < 2.598400643880996e-100 or 5.1343243090214894e+57 < (cbrt (/ z y))

    1. Initial program 24.6

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

    2. Applied simplify18.3

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

    4. Applied associate-/r/0.9

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

    if (cbrt (/ z y)) < -4.353809244386929e-70 or 2.598400643880996e-100 < (cbrt (/ z y)) < 5.1343243090214894e+57

    1. Initial program 9.7

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

    2. Applied simplify0.2

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

Runtime

Time bar (total: 13.3s)Debug logProfile

herbie shell --seed '#(1064269945 2896236262 301053905 1701069080 1701464310 1614783279)' +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)))