Average Error: 14.0 → 1.4
Time: 21.8s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -2.6267834257930744 \cdot 10^{+158}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -1.7454457668307553 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 5.94691164027304 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 9.402888763165793 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (/ (* (/ y z) t) t) < -2.6267834257930744e+158

    1. Initial program 36.8

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

    2. Initial simplification2.5

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

    4. Applied associate-*r/3.8

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

    if -2.6267834257930744e+158 < (/ (* (/ y z) t) t) < -1.7454457668307553e-166 or 5.94691164027304e-247 < (/ (* (/ y z) t) t) < 9.402888763165793e+148

    1. Initial program 0.6

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

    if -1.7454457668307553e-166 < (/ (* (/ y z) t) t) < 5.94691164027304e-247 or 9.402888763165793e+148 < (/ (* (/ y z) t) t)

    1. Initial program 25.5

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

    2. Initial simplification1.9

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -2.6267834257930744 \cdot 10^{+158}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -1.7454457668307553 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 5.94691164027304 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 9.402888763165793 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Runtime

Time bar (total: 21.8s)Debug logProfile

herbie shell --seed 2018248 +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)))