?

Average Error: 0.0 → 0.0
Time: 6.4s
Precision: binary64
Cost: 704

?

\[\frac{x + y}{x - y} \]
↓
\[\frac{y}{x - y} + \frac{x}{x - y} \]
(FPCore (x y) :precision binary64 (/ (+ x y) (- x y)))
↓
(FPCore (x y) :precision binary64 (+ (/ y (- x y)) (/ x (- x y))))
double code(double x, double y) {
	return (x + y) / (x - y);
}
↓
double code(double x, double y) {
	return (y / (x - y)) + (x / (x - y));
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / (x - y)
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y / (x - y)) + (x / (x - y))
end function

public static double code(double x, double y) {
	return (x + y) / (x - y);
}
↓
public static double code(double x, double y) {
	return (y / (x - y)) + (x / (x - y));
}

def code(x, y):
	return (x + y) / (x - y)
↓
def code(x, y):
	return (y / (x - y)) + (x / (x - y))

function code(x, y)
	return Float64(Float64(x + y) / Float64(x - y))
end
↓
function code(x, y)
	return Float64(Float64(y / Float64(x - y)) + Float64(x / Float64(x - y)))
end

function tmp = code(x, y)
	tmp = (x + y) / (x - y);
end
↓
function tmp = code(x, y)
	tmp = (y / (x - y)) + (x / (x - y));
end

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision] + N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{x + y}{x - y}
↓
\frac{y}{x - y} + \frac{x}{x - y}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation?

  1. Initial program 0.0

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

  2. Applied egg-rr0.2

    \[\leadsto \color{blue}{\frac{1}{x - y} \cdot \left(x + y\right)} \]

  3. Applied egg-rr0.0

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

  4. Final simplification0.0

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

Alternatives

Alternative 1
Error16.0
Cost977
\[\begin{array}{l} t_0 := -2 \cdot \frac{x}{y} + -1\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-33}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+30}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+73} \lor \neg \left(y \leq 1.4 \cdot 10^{+99}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 2
Error16.4
Cost712
\[\begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-32}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+34}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+73}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+98}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
Alternative 3
Error16.7
Cost592
\[\begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-34}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+27}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+73}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+99}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
Alternative 4
Error0.0
Cost576
\[\frac{1}{\frac{x - y}{y + x}} \]
Alternative 5
Error0.0
Cost448
\[\frac{y + x}{x - y} \]
Alternative 6
Error32.7
Cost64
\[-1 \]

Error

Reproduce?

herbie shell --seed 2023018 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

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

  (/ (+ x y) (- x y)))