(/ (+ x (- (* (- y1) y2) (- (* z1 z2) (* w1 w2)))) a)

Average Error: 11.7 → 11.7

Time: 2.3s

Precision: binary64

Math

\[\frac{x + \left(\left(-y1\right) \cdot y2 - \left(z1 \cdot z2 - w1 \cdot w2\right)\right)}{a}\]

↓

\[\frac{x + \left(\left(-y1\right) \cdot y2 - \left(z1 \cdot z2 - w1 \cdot w2\right)\right)}{a}\]

Error

Bits error versus x

Bits error versus y1

Bits error versus y2

Bits error versus z1

Bits error versus z2

Bits error versus w1

Bits error versus w2

Bits error versus a

Derivation

1. Initial program 11.7

   \[\frac{x + \left(\left(-y1\right) \cdot y2 - \left(z1 \cdot z2 - w1 \cdot w2\right)\right)}{a}\]

2. Final simplification 11.7

   \[\leadsto \frac{x + \left(\left(-y1\right) \cdot y2 - \left(z1 \cdot z2 - w1 \cdot w2\right)\right)}{a}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y1 y2 z1 z2 w1 w2 a)
  :name "(/ (+ x (- (* (- y1) y2) (- (* z1 z2) (* w1 w2)))) a)"
  :precision binary64
  (/ (+ x (- (* (neg y1) y2) (- (* z1 z2) (* w1 w2)))) a))