Average Error: 14.5 → 0.5
Time: 12.5s
Precision: 64
Internal Precision: 384
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{if}\;\frac{y}{z} \le -7.286146902991541 \cdot 10^{-134}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;\frac{y}{z} \le 7.14869194418827 \cdot 10^{-254}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{if}\;\frac{y}{z} \le 1.268364041880251 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

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 (/ y z) < -inf.0

    1. Initial program 59.9

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

    2. Applied simplify56.2

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

    4. Applied div-inv59.9

      \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{z}{y}}}\]

    5. Applied simplify59.9

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

    7. Applied div-inv59.9

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)}\]

    8. Applied associate-*r*0.3

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]

    if -inf.0 < (/ y z) < -7.286146902991541e-134 or 7.14869194418827e-254 < (/ y z) < 1.268364041880251e+212

    1. Initial program 9.2

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

    2. Applied simplify0.2

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

    4. Applied div-inv0.3

      \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{z}{y}}}\]

    5. Applied simplify0.2

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

    if -7.286146902991541e-134 < (/ y z) < 7.14869194418827e-254

    1. Initial program 16.8

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

    2. Applied simplify11.0

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

    4. Applied div-inv11.0

      \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{z}{y}}}\]

    5. Applied simplify10.1

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

    7. Applied div-inv10.2

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)}\]

    8. Applied associate-*r*1.1

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]

    if 1.268364041880251e+212 < (/ y z)

    1. Initial program 41.1

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

    2. Applied simplify25.6

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

    3. Taylor expanded around 0 0.6

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

Runtime

Time bar (total: 12.5s)Debug logProfile

herbie shell --seed '#(1070227846 1561819246 480764335 4016816270 2602869839 2117310382)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))