Average Error: 14.3 → 1.6
Time: 6.8s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -8.554197246439074 \cdot 10^{+236}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -7.092775599795027 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 0.0:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 5.396660912025774 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Results

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Derivation

  1. Split input into 4 regimes

  2. if (/ (* (/ y z) t) t) < -8.554197246439074e+236

    1. Initial program 50.0

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

    2. Initial simplification3.8

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

    4. Applied associate-*r/2.2

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

    6. Applied associate-/l*3.4

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

    if -8.554197246439074e+236 < (/ (* (/ y z) t) t) < -7.092775599795027e-119 or 0.0 < (/ (* (/ y z) t) t) < 5.396660912025774e+162

    1. Initial program 0.7

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

    if -7.092775599795027e-119 < (/ (* (/ y z) t) t) < 0.0

    1. Initial program 21.1

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

    2. Initial simplification1.8

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

    4. Applied div-inv1.9

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

    5. Applied associate-*r*2.2

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

    if 5.396660912025774e+162 < (/ (* (/ y z) t) t)

    1. Initial program 39.5

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

    2. Initial simplification3.4

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -8.554197246439074 \cdot 10^{+236}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -7.092775599795027 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 0.0:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 5.396660912025774 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Runtime

Time bar (total: 6.8s)Debug logProfile

herbie shell --seed 2018220 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))