Average Error: 0.0 → 0.0
Time: 3.1s
Precision: binary64
\[x + \frac{y - x}{z} \]
↓
\[x - \frac{x - y}{z} \]
x + \frac{y - x}{z}
↓
x - \frac{x - y}{z}

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))
↓
(FPCore (x y z) :precision binary64 (- x (/ (- x y) z)))
double code(double x, double y, double z) {
	return x + ((y - x) / z);
}
↓
double code(double x, double y, double z) {
	return x - ((x - y) / z);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x + \frac{y - x}{z} \]

  2. Taylor expanded in y around 0 0.0

    \[\leadsto x + \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} \]

  3. Taylor expanded in z around -inf 0.0

    \[\leadsto x + \color{blue}{-1 \cdot \frac{x - y}{z}} \]

  4. Simplified0.0

    \[\leadsto x + \color{blue}{\left(-\frac{x - y}{z}\right)} \]

  5. Final simplification0.0

    \[\leadsto x - \frac{x - y}{z} \]

Reproduce

herbie shell --seed 2022077 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))