Average Error: 0.0 → 0.0
Time: 1000.0ms
Precision: binary64
\[\frac{x - y}{x} \]
↓
\[1 - \frac{y}{x} \]
\frac{x - y}{x}
↓
1 - \frac{y}{x}

(FPCore (x y) :precision binary64 (/ (- x y) x))
↓
(FPCore (x y) :precision binary64 (- 1.0 (/ y x)))
double code(double x, double y) {
	return (x - y) / x;
}
↓
double code(double x, double y) {
	return 1.0 - (y / x);
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[1 - \frac{y}{x} \]

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded in x around 0 0.0

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

  3. Final simplification0.0

    \[\leadsto 1 - \frac{y}{x} \]

Reproduce

herbie shell --seed 2022081 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- 1.0 (/ y x))

  (/ (- x y) x))