Average Error: 13.9 → 0.3
Time: 15.9s
Precision: 64
Internal Precision: 384
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\sqrt[3]{\frac{z}{y}} \le -1.6616659312894043 \cdot 10^{+74}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{if}\;\sqrt[3]{\frac{z}{y}} \le -1.6007854891772637 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\sqrt[3]{\frac{z}{y}} \le 7.646065832775904 \cdot 10^{-74}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{if}\;\sqrt[3]{\frac{z}{y}} \le 2.1640454249062944 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Split input into 4 regimes

  2. if (cbrt (/ z y)) < -1.6616659312894043e+74 or -1.6007854891772637e-90 < (cbrt (/ z y)) < 7.646065832775904e-74

    1. Initial program 29.5

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

    2. Applied simplify19.8

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

    3. Taylor expanded around 0 0.7

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

    if -1.6616659312894043e+74 < (cbrt (/ z y)) < -1.6007854891772637e-90

    1. Initial program 9.0

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

    2. Applied simplify0.2

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

    if 7.646065832775904e-74 < (cbrt (/ z y)) < 2.1640454249062944e+81

    1. Initial program 8.4

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

    2. Applied simplify0.2

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

    if 2.1640454249062944e+81 < (cbrt (/ z y))

    1. Initial program 17.7

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

    2. Applied simplify13.1

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

    4. Applied associate-/r/0.2

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

Runtime

Time bar (total: 15.9s)Debug logProfile

herbie shell --seed '#(1064300848 3212030778 2049303162 3567222883 2277747821 1384278011)' +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)))