Average Error: 15.0 → 1.5
Time: 5.8s
Precision: 64
Internal Precision: 320
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} = -\infty:\\ \;\;\;\;\frac{1}{z} \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -1.7722923631317696 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 9.527790533614926 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 2.1507009231764657 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

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Bits error versus y

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Results

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Derivation

  1. Split input into 5 regimes

  2. if (/ (* (/ y z) t) t) < -inf.0

    1. Initial program 60.7

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

    2. Initial simplification4.3

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

    4. Applied div-inv4.4

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

    5. Applied associate-*r*3.4

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

    if -inf.0 < (/ (* (/ y z) t) t) < -1.7722923631317696e-85

    1. Initial program 0.5

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

    2. Initial simplification9.5

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

    4. Applied associate-*r/10.7

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

    6. Applied associate-/l*9.5

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

    8. Applied div-inv9.6

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

    9. Applied associate-/r*0.4

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

    if -1.7722923631317696e-85 < (/ (* (/ y z) t) t) < 9.527790533614926e-253

    1. Initial program 19.6

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

    2. Initial simplification1.9

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

    if 9.527790533614926e-253 < (/ (* (/ y z) t) t) < 2.1507009231764657e+176

    1. Initial program 0.7

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

    if 2.1507009231764657e+176 < (/ (* (/ y z) t) t)

    1. Initial program 40.4

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

    2. Initial simplification3.1

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

    4. Applied associate-*r/3.0

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} = -\infty:\\ \;\;\;\;\frac{1}{z} \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -1.7722923631317696 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 9.527790533614926 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 2.1507009231764657 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Runtime

Time bar (total: 5.8s)Debug logProfile

herbie shell --seed 2018225 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))