Average Error: 14.8 → 3.9
Time: 40.3s
Precision: 64
Internal Precision: 384
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -5.562216828736827 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -0.0:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le 5.331406091691036 \cdot 10^{-149}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le 1.2941480283956699 \cdot 10^{+210}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Split input into 3 regimes

  2. if (/ (* (/ y z) t) t) < -5.562216828736827e+106 or -0.0 < (/ (* (/ y z) t) t) < 5.331406091691036e-149

    1. Initial program 20.0

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

    2. Applied simplify8.3

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

    4. Applied associate-/r/3.0

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

    if -5.562216828736827e+106 < (/ (* (/ y z) t) t) < -0.0 or 5.331406091691036e-149 < (/ (* (/ y z) t) t) < 1.2941480283956699e+210

    1. Initial program 9.6

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

    2. Applied simplify4.3

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

    if 1.2941480283956699e+210 < (/ (* (/ y z) t) t)

    1. Initial program 47.7

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

    2. Applied simplify18.3

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

    4. Applied associate-/r/2.9

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

Runtime

Time bar (total: 40.3s)Debug logProfile

herbie shell --seed '#(1063313015 2771194459 1594909340 1344785158 2223560818 546365448)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))