(/ (* (- (+ 331.4 (* 0.6 T))) v) (* (+ (+ 331.4 (* 0.6 T)) u) (+ (+ 331.4 (* 0.6 T)) u)))

Average Error: 14.7 → 14.7

Time: 1.1s

Precision: binary64

Math

\[\frac{\left(-\left(331.39999999999998 + 0.599999999999999978 \cdot T\right)\right) \cdot v}{\left(\left(331.39999999999998 + 0.599999999999999978 \cdot T\right) + u\right) \cdot \left(\left(331.39999999999998 + 0.599999999999999978 \cdot T\right) + u\right)}\]

↓

\[\frac{\left(-\left(331.39999999999998 + 0.599999999999999978 \cdot T\right)\right) \cdot v}{\left(\left(331.39999999999998 + 0.599999999999999978 \cdot T\right) + u\right) \cdot \left(\left(331.39999999999998 + 0.599999999999999978 \cdot T\right) + u\right)}\]

Error

Bits error versus T

Bits error versus v

Bits error versus u

Derivation

1. Initial program 14.7

   \[\frac{\left(-\left(331.39999999999998 + 0.599999999999999978 \cdot T\right)\right) \cdot v}{\left(\left(331.39999999999998 + 0.599999999999999978 \cdot T\right) + u\right) \cdot \left(\left(331.39999999999998 + 0.599999999999999978 \cdot T\right) + u\right)}\]

2. Final simplification 14.7

   \[\leadsto \frac{\left(-\left(331.39999999999998 + 0.599999999999999978 \cdot T\right)\right) \cdot v}{\left(\left(331.39999999999998 + 0.599999999999999978 \cdot T\right) + u\right) \cdot \left(\left(331.39999999999998 + 0.599999999999999978 \cdot T\right) + u\right)}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (T v u)
  :name "(/ (* (- (+ 331.4 (* 0.6 T))) v) (* (+ (+ 331.4 (* 0.6 T)) u) (+ (+ 331.4 (* 0.6 T)) u)))"
  :precision binary64
  (/ (* (neg (+ 331.4 (* 0.6 T))) v) (* (+ (+ 331.4 (* 0.6 T)) u) (+ (+ 331.4 (* 0.6 T)) u))))