Average Error: 1.7 → 3.1
Time: 22.8s
Precision: 64
Internal Precision: 576
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\left(x + 4\right) \cdot \frac{1}{y} - \frac{x}{\frac{y}{z}}\right|\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.7

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

  2. Initial simplification3.0

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

  4. Applied div-inv3.1

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

  5. Final simplification3.1

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

Runtime

Time bar (total: 22.8s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes3.13.10.03.10%
herbie shell --seed 2018297 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))