Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 76.7% → 99.7%

Time: 6.0s

Precision: binary64

Cost: 841

Math

\[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+60} \lor \neg \left(y \leq 2 \cdot 10^{+23}\right):\\ \;\;\;\;x \cdot \frac{2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))

↓

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.4e+60) (not (<= y 2e+23)))
   (* x (/ 2.0 (/ (- x y) y)))
   (* y (/ (* x 2.0) (- x y)))))

C

double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

↓

double code(double x, double y) {
	double tmp;
	if ((y <= -3.4e+60) || !(y <= 2e+23)) {
		tmp = x * (2.0 / ((x - y) / y));
	} else {
		tmp = y * ((x * 2.0) / (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) * y) / (x - y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-3.4d+60)) .or. (.not. (y <= 2d+23))) then
        tmp = x * (2.0d0 / ((x - y) / y))
    else
        tmp = y * ((x * 2.0d0) / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

↓

public static double code(double x, double y) {
	double tmp;
	if ((y <= -3.4e+60) || !(y <= 2e+23)) {
		tmp = x * (2.0 / ((x - y) / y));
	} else {
		tmp = y * ((x * 2.0) / (x - y));
	}
	return tmp;
}

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

↓

def code(x, y):
	tmp = 0
	if (y <= -3.4e+60) or not (y <= 2e+23):
		tmp = x * (2.0 / ((x - y) / y))
	else:
		tmp = y * ((x * 2.0) / (x - y))
	return tmp

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
end

↓

function code(x, y)
	tmp = 0.0
	if ((y <= -3.4e+60) || !(y <= 2e+23))
		tmp = Float64(x * Float64(2.0 / Float64(Float64(x - y) / y)));
	else
		tmp = Float64(y * Float64(Float64(x * 2.0) / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) * y) / (x - y);
end

↓

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3.4e+60) || ~((y <= 2e+23)))
		tmp = x * (2.0 / ((x - y) / y));
	else
		tmp = y * ((x * 2.0) / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := If[Or[LessEqual[y, -3.4e+60], N[Not[LessEqual[y, 2e+23]], $MachinePrecision]], N[(x * N[(2.0 / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	76.7%
Target	99.5%
Herbie	99.7%

\[\begin{array}{l} \mathbf{if}\;x < -1.7210442634149447 \cdot 10^{+81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x < 83645045635564430:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if y < -3.4e60 or 1.9999999999999998e23 < y

   1. Initial program 78.0%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]

   2. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{2}{\frac{x - y}{y}}} \]
      Step-by-step derivation

      [Start] 78.0%	\[ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
      associate-/l* [=>] 100.0%	\[ \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]
      associate-*r/ [<=] 99.9%	\[ \color{blue}{x \cdot \frac{2}{\frac{x - y}{y}}} \]

   if -3.4e60 < y < 1.9999999999999998e23

   1. Initial program 89.8%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]

   2. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{x - y} \cdot y} \]
      Step-by-step derivation

      [Start] 89.8%	\[ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
      associate-*l/ [<=] 100.0%	\[ \color{blue}{\frac{x \cdot 2}{x - y} \cdot y} \]

3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+60} \lor \neg \left(y \leq 2 \cdot 10^{+23}\right):\\ \;\;\;\;x \cdot \frac{2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+60} \lor \neg \left(y \leq 2 \cdot 10^{+23}\right):\\ \;\;\;\;x \cdot \frac{2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \end{array} \]

Alternative 2
Accuracy	93.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-165} \lor \neg \left(y \leq 2 \cdot 10^{-110}\right):\\ \;\;\;\;x \cdot \frac{2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]

Alternative 3
Accuracy	73.9%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-64}:\\ \;\;\;\;x \cdot -2\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+64}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \]

Alternative 4
Accuracy	50.8%
Cost	192

\[y \cdot 2 \]

Reproduce

herbie shell --seed 2023263 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e+81) (* (/ (* 2.0 x) (- x y)) y) (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) (* (/ (* 2.0 x) (- x y)) y)))

  (/ (* (* x 2.0) y) (- x y)))