Linear.Projection:perspective from linear-1.19.1.3, A

Average Error: 0.0 → 0.0

Time: 6.5s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) (- x y)))

↓

(FPCore (x y) :precision binary64 (/ (+ x y) (- x y)))

C

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

↓

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

Fortran

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 = (x + y) / (x - y)
end function

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	20.1
Cost	978

\[\begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+86} \lor \neg \left(x \leq -3.3 \cdot 10^{-95}\right) \land \left(x \leq -1.1 \cdot 10^{-136} \lor \neg \left(x \leq 5.2 \cdot 10^{+143}\right)\right):\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 2
Error	17.7
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+129}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+26}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-26}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3
Error	32.5
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2022364 
(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)))