Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[x + y \cdot \left(z - x\right)\]
↓
\[\left(x + z \cdot y\right) + y \cdot \left(-x\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x + y \cdot \left(z - x\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

    \[\leadsto \left(x + z \cdot y\right) + y \cdot \left(-x\right)\]

Reproduce

herbie shell --seed 2020150 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))