Average Error: 0.0 → 0.0
Time: 3.4s
Precision: binary64
Cost: 576
\[\frac{x + y}{x - y} \]
↓
\[\frac{1}{\frac{x - y}{x + y}} \]
(FPCore (x y) :precision binary64 (/ (+ x y) (- x y)))
↓
(FPCore (x y) :precision binary64 (/ 1.0 (/ (- x y) (+ x y))))
double code(double x, double y) {
	return (x + y) / (x - y);
}
↓
double code(double x, double y) {
	return 1.0 / ((x - y) / (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 = 1.0d0 / ((x - y) / (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 1.0 / ((x - y) / (x + y));
}

def code(x, y):
	return (x + y) / (x - y)
↓
def code(x, y):
	return 1.0 / ((x - y) / (x + y))

function code(x, y)
	return Float64(Float64(x + y) / Float64(x - y))
end
↓
function code(x, y)
	return Float64(1.0 / Float64(Float64(x - y) / Float64(x + y)))
end

function tmp = code(x, y)
	tmp = (x + y) / (x - y);
end
↓
function tmp = code(x, y)
	tmp = 1.0 / ((x - y) / (x + y));
end

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(1.0 / N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{x + y}{x - y}
↓
\frac{1}{\frac{x - y}{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-rr0.0

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

  3. Applied egg-rr0.0

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

  4. Final simplification0.0

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

Alternatives

Alternative 1
Error16.7
Cost1507
\[\begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+119}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+65} \lor \neg \left(y \leq -1950000000\right) \land \left(y \leq 6.5 \cdot 10^{-86} \lor \neg \left(y \leq 2.2 \cdot 10^{-67}\right) \land \left(y \leq 45000 \lor \neg \left(y \leq 1.25 \cdot 10^{+41}\right) \land y \leq 4.4 \cdot 10^{+59}\right)\right):\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
Alternative 2
Error16.4
Cost1504
\[\begin{array}{l} t_0 := -2 \cdot \frac{x}{y} + -1\\ t_1 := 1 + 2 \cdot \frac{y}{x}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+119}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3700000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-67}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 4800:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+50}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error16.7
Cost1120
\[\begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+92}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 10^{-87}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-67}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1500:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+44}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+57}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
Alternative 4
Error0.0
Cost448
\[\frac{x + y}{x - y} \]
Alternative 5
Error32.9
Cost64
\[-1 \]

Error

Reproduce

herbie shell --seed 2023016 
(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)))