Average Error: 1.6 → 1.6
Time: 9.1s
Precision: 64
Internal Precision: 320
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{1}{\frac{y}{4 + x}} - \frac{x}{y} \cdot z\right|\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.6

    \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
  2. Using strategy rm

  3. Applied clear-num1.6

    \[\leadsto \left|\color{blue}{\frac{1}{\frac{y}{x + 4}}} - \frac{x}{y} \cdot z\right|\]

  4. Final simplification1.6

    \[\leadsto \left|\frac{1}{\frac{y}{4 + x}} - \frac{x}{y} \cdot z\right|\]

Runtime

Time bar (total: 9.1s)Debug logProfile

herbie shell --seed 2018219 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))