(- (- (- az dz) (* (/ vz vx) (- ax dx))))

Average Error: 1.6 → 1.6

Time: 1.5s

Precision: binary64

Math

\[-\left(\left(az - dz\right) - \frac{vz}{vx} \cdot \left(ax - dx\right)\right)\]

↓

\[\frac{vz}{vx} \cdot \left(ax - dx\right) - \left(az - dz\right)\]

Error

Bits error versus az

Bits error versus dz

Bits error versus vz

Bits error versus vx

Bits error versus ax

Bits error versus dx

Derivation

1. Initial program 1.6

   \[-\left(\left(az - dz\right) - \frac{vz}{vx} \cdot \left(ax - dx\right)\right)\]

2. Simplified 1.6

   \[\leadsto \color{blue}{\frac{vz}{vx} \cdot \left(ax - dx\right) - \left(az - dz\right)}\]

3. Final simplification 1.6

   \[\leadsto \frac{vz}{vx} \cdot \left(ax - dx\right) - \left(az - dz\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (az dz vz vx ax dx)
  :name "(- (- (- az dz) (* (/ vz vx) (- ax dx))))"
  :precision binary64
  (neg (- (- az dz) (* (/ vz vx) (- ax dx)))))