Linear.Projection:perspective from linear-1.19.1.3, A

Average Error: 0.0 → 0.0

Time: 3.1s

Precision: binary64

Cost: 13248

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double x, double y) {
	return log(exp(((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 = log(exp(((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 Math.log(Math.exp(((x + y) / (x - y))));
}

Python

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

↓

def code(x, y):
	return math.log(math.exp(((x + y) / (x - y))))

Julia

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

↓

function code(x, y)
	return log(exp(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 = log(exp(((x + y) / (x - y))));
end

Wolfram

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

↓

code[x_, y_] := N[Log[N[Exp[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. Final simplification 0.0

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

Alternatives

Alternative 1
Error	17.0
Cost	1240

\[\begin{array}{l} t_0 := -2 \cdot \frac{x}{y} + -1\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+39}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.15 \cdot 10^{-41}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-66}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{-37}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	17.4
Cost	856

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+70}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+38}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-38}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 10^{-72}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-39}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3
Error	0.0
Cost	448

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

Alternative 4
Error	32.6
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2022329 
(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)))