Linear.Projection:perspective from linear-1.19.1.3, A

Average Error: 0.0 → 0.0

Time: 6.4s

Precision: binary64

Cost: 704

Math

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

↓

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

FPCore

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

↓

(FPCore (x y) :precision binary64 (/ 1.0 (/ 1.0 (/ (+ x y) (- x y)))))

C

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

↓

double code(double x, double y) {
	return 1.0 / (1.0 / ((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 = 1.0d0 / (1.0d0 / ((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 1.0 / (1.0 / ((x + y) / (x - y)));
}

Python

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

code[x_, y_] := N[(1.0 / N[(1.0 / N[(N[(x + y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $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. Applied egg-rr 0.0

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

3. Applied egg-rr 0.2

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

4. Applied egg-rr 0.0

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

5. Final simplification 0.0

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

Alternatives

Alternative 1
Error	16.7
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-29} \lor \neg \left(y \leq 9.5 \cdot 10^{+68}\right):\\ \;\;\;\;-2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \end{array} \]

Alternative 2
Error	17.3
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-26}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+73}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3
Error	0.0
Cost	448

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

Alternative 4
Error	17.5
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-25}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+68}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5
Error	32.3
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023066 
(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)))