Average Error: 13.7 → 1.1
Time: 18.8s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -3.464233194755603 \cdot 10^{+242}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -4.783679638020658 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 6.22797790474625 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 1.5103871131255598 \cdot 10^{+283}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

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 2 regimes

  2. if (/ (* (/ y z) t) t) < -3.464233194755603e+242 or -4.783679638020658e-170 < (/ (* (/ y z) t) t) < 6.22797790474625e-254 or 1.5103871131255598e+283 < (/ (* (/ y z) t) t)

    1. Initial program 30.6

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

    2. Initial simplification1.8

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

    if -3.464233194755603e+242 < (/ (* (/ y z) t) t) < -4.783679638020658e-170 or 6.22797790474625e-254 < (/ (* (/ y z) t) t) < 1.5103871131255598e+283

    1. Initial program 0.6

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -3.464233194755603 \cdot 10^{+242}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -4.783679638020658 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 6.22797790474625 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 1.5103871131255598 \cdot 10^{+283}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Runtime

Time bar (total: 18.8s)Debug logProfile

herbie shell --seed 2018230 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))