(- (- (- bz az) (* (/ vz vx) (- bx ax))))

Average Error: 1.8 → 1.8

Time: 1.5s

Precision: binary64

Math

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

↓

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

Error

Bits error versus bz

Bits error versus az

Bits error versus vz

Bits error versus vx

Bits error versus bx

Bits error versus ax

Derivation

1. Initial program 1.8

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

2. Simplified 1.8

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

3. Final simplification 1.8

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

Reproduce

herbie shell --seed 2020153 
(FPCore (bz az vz vx bx ax)
  :name "(- (- (- bz az) (* (/ vz vx) (- bx ax))))"
  :precision binary64
  (neg (- (- bz az) (* (/ vz vx) (- bx ax)))))