Average Error: 13.9 → 0.8
Time: 28.4s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.7265094403537214 \cdot 10^{+144}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.6288018572505108 \cdot 10^{-251}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 2.8784423652490492 \cdot 10^{-211}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 4.2827272105516214 \cdot 10^{+128}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (/ y z) < -3.7265094403537214e+144

    1. Initial program 32.9

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

    2. Initial simplification17.9

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

    4. Applied associate-*l/2.6

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

    6. Applied associate-/l*2.6

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

    if -3.7265094403537214e+144 < (/ y z) < -2.6288018572505108e-251 or 2.8784423652490492e-211 < (/ y z) < 4.2827272105516214e+128

    1. Initial program 6.7

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

    2. Initial simplification0.2

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

    if -2.6288018572505108e-251 < (/ y z) < 2.8784423652490492e-211 or 4.2827272105516214e+128 < (/ y z)

    1. Initial program 21.0

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

    2. Initial simplification12.9

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

    4. Applied associate-*l/1.3

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.7265094403537214 \cdot 10^{+144}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.6288018572505108 \cdot 10^{-251}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 2.8784423652490492 \cdot 10^{-211}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 4.2827272105516214 \cdot 10^{+128}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Runtime

Time bar (total: 28.4s)Debug logProfile

herbie shell --seed 2018214 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))