Average Error: 13.9 → 0.3
Time: 16.3s
Precision: 64
Internal Precision: 384
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\sqrt[3]{\frac{z}{y}} \le -4.187492351566737 \cdot 10^{+74}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{if}\;\sqrt[3]{\frac{z}{y}} \le -6.33648606231181 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\sqrt[3]{\frac{z}{y}} \le 7.646065832775904 \cdot 10^{-74}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{if}\;\sqrt[3]{\frac{z}{y}} \le 2.827883909163644 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

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)) < -4.187492351566737e+74 or -6.33648606231181e-91 < (cbrt (/ z y)) < 7.646065832775904e-74

    1. Initial program 29.5

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

    2. Applied simplify19.9

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

    3. Taylor expanded around 0 0.7

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

    if -4.187492351566737e+74 < (cbrt (/ z y)) < -6.33648606231181e-91

    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)) < 2.827883909163644e+82

    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 2.827883909163644e+82 < (cbrt (/ z y))

    1. Initial program 17.7

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

    2. Applied simplify13.3

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
    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: 16.3s)Debug logProfile

herbie shell --seed '#(1064300848 3212030778 2049303162 3567222883 2277747821 1384278011)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))