(/ (- (+ (+ (* a x0) (* b y0)) (* c z0))) (+ (+ (* a x1) (* b y1)) (* c z1)))

Average Error: 27.3 → 27.3

Time: 2.1s

Precision: binary64

Math

\[\frac{-\left(\left(a \cdot x0 + b \cdot y0\right) + c \cdot z0\right)}{\left(a \cdot x1 + b \cdot y1\right) + c \cdot z1}\]

↓

\[\frac{-\left(\left(a \cdot x0 + b \cdot y0\right) + c \cdot z0\right)}{\left(a \cdot x1 + b \cdot y1\right) + c \cdot z1}\]

Error

Bits error versus a

Bits error versus x0

Bits error versus b

Bits error versus y0

Bits error versus c

Bits error versus z0

Bits error versus x1

Bits error versus y1

Bits error versus z1

Derivation

1. Initial program 27.3

   \[\frac{-\left(\left(a \cdot x0 + b \cdot y0\right) + c \cdot z0\right)}{\left(a \cdot x1 + b \cdot y1\right) + c \cdot z1}\]

2. Final simplification 27.3

   \[\leadsto \frac{-\left(\left(a \cdot x0 + b \cdot y0\right) + c \cdot z0\right)}{\left(a \cdot x1 + b \cdot y1\right) + c \cdot z1}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a x0 b y0 c z0 x1 y1 z1)
  :name "(/ (- (+ (+ (* a x0) (* b y0)) (* c z0))) (+ (+ (* a x1) (* b y1)) (* c z1)))"
  :precision binary64
  (/ (neg (+ (+ (* a x0) (* b y0)) (* c z0))) (+ (+ (* a x1) (* b y1)) (* c z1))))