Average Error: 0.0 → 0.0
Time: 1.2s
Precision: binary64
Cost: 320
\[\frac{x - y}{x}\]
↓
\[1 - \frac{y}{x}\]
\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
\[1 - \frac{y}{x}\]

Alternatives

Alternative 1
Error0.0
Cost320
\[\frac{x - y}{x}\]
Alternative 2
Error18.7
Cost1114
\[\begin{array}{l} \mathbf{if}\;y \leq -3.2247188086597996 \cdot 10^{+113} \lor \neg \left(y \leq -5676673098700.002 \lor \neg \left(y \leq -1.447122502976968 \cdot 10^{-18}\right) \land \left(y \leq -1.9817070940739126 \cdot 10^{-98} \lor \neg \left(y \leq -6.722961088239449 \cdot 10^{-109}\right) \land y \leq 2.7691887228546377 \cdot 10^{+24}\right)\right):\\ \;\;\;\;\frac{y}{-x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 3
Error27.1
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x}\]
  2. Using strategy rm

  3. Applied div-sub_binary64_174740.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(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))