Linear.Projection:perspective from linear-1.19.1.3, A

Average Accuracy: 100.0% → 100.0%

Time: 10.0s

Precision: binary64

Cost: 832

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Python

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

↓

def code(x, y):
	return 1.0 / ((x / (x + y)) - (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(Float64(x / Float64(x + y)) - Float64(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 / ((x / (x + y)) - (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[(N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	100.0%
Target	100.0%
Herbie	100.0%

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

Derivation

1. Initial program 100.0%

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

2. Applied egg-rr 100.0%

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

   [Start] 100.0	\[ \frac{x + y}{x - y} \]
   clear-num [=>] 100.0	\[ \color{blue}{\frac{1}{\frac{x - y}{x + y}}} \]
   inv-pow [=>] 100.0	\[ \color{blue}{{\left(\frac{x - y}{x + y}\right)}^{-1}} \]

3. Applied egg-rr 100.0%

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

   [Start] 100.0	\[ {\left(\frac{x - y}{x + y}\right)}^{-1} \]
   unpow-1 [=>] 100.0	\[ \color{blue}{\frac{1}{\frac{x - y}{x + y}}} \]

4. Applied egg-rr 100.0%

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

   [Start] 100.0	\[ \frac{1}{\frac{x - y}{x + y}} \]
   div-sub [=>] 100.0	\[ \frac{1}{\color{blue}{\frac{x}{x + y} - \frac{y}{x + y}}} \]

5. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	72.1%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+89} \lor \neg \left(x \leq 9.8 \cdot 10^{+113}\right):\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 2
Accuracy	72.7%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+90} \lor \neg \left(x \leq 9.8 \cdot 10^{+113}\right):\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{y} + -1\\ \end{array} \]

Alternative 3
Accuracy	100.0%
Cost	448

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

Alternative 4
Accuracy	71.6%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+89}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+113}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Accuracy	49.8%
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2023151 
(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)))