Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 76.9% → 98.9%

Time: 4.5s

Alternatives: 5

Speedup: 0.7×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \end{array} \]

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \end{array} \]

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x - y} \cdot \left(2 \cdot y\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{-130}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{x - y} \cdot {\left({\left(2 \cdot x\right)}^{-1}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ x (- x y)) (* 2.0 y))))
   (if (<= x -6.5e-130)
     t_0
     (if (<= x 5e-64) (* (/ y (- x y)) (pow (pow (* 2.0 x) -1.0) -1.0)) t_0))))

C

double code(double x, double y) {
	double t_0 = (x / (x - y)) * (2.0 * y);
	double tmp;
	if (x <= -6.5e-130) {
		tmp = t_0;
	} else if (x <= 5e-64) {
		tmp = (y / (x - y)) * pow(pow((2.0 * x), -1.0), -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x / (x - y)) * (2.0d0 * y)
    if (x <= (-6.5d-130)) then
        tmp = t_0
    else if (x <= 5d-64) then
        tmp = (y / (x - y)) * (((2.0d0 * x) ** (-1.0d0)) ** (-1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x / (x - y)) * (2.0 * y);
	double tmp;
	if (x <= -6.5e-130) {
		tmp = t_0;
	} else if (x <= 5e-64) {
		tmp = (y / (x - y)) * Math.pow(Math.pow((2.0 * x), -1.0), -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x / (x - y)) * (2.0 * y)
	tmp = 0
	if x <= -6.5e-130:
		tmp = t_0
	elif x <= 5e-64:
		tmp = (y / (x - y)) * math.pow(math.pow((2.0 * x), -1.0), -1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x / Float64(x - y)) * Float64(2.0 * y))
	tmp = 0.0
	if (x <= -6.5e-130)
		tmp = t_0;
	elseif (x <= 5e-64)
		tmp = Float64(Float64(y / Float64(x - y)) * ((Float64(2.0 * x) ^ -1.0) ^ -1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x / (x - y)) * (2.0 * y);
	tmp = 0.0;
	if (x <= -6.5e-130)
		tmp = t_0;
	elseif (x <= 5e-64)
		tmp = (y / (x - y)) * (((2.0 * x) ^ -1.0) ^ -1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision] * N[(2.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.5e-130], t$95$0, If[LessEqual[x, 5e-64], N[(N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision] * N[Power[N[Power[N[(2.0 * x), $MachinePrecision], -1.0], $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5000000000000002e-130 or 5.00000000000000033e-64 < x

   1. Initial program 82.6%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   if -6.5000000000000002e-130 < x < 5.00000000000000033e-64

   1. Initial program 74.2%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{x - y}{\left(x \cdot 2\right) \cdot y}}} \]

      3. inv-pow N/A

         \[\leadsto \color{blue}{{\left(\frac{x - y}{\left(x \cdot 2\right) \cdot y}\right)}^{-1}} \]

      4. frac-2neg N/A

         \[\leadsto {\color{blue}{\left(\frac{\mathsf{neg}\left(\left(x - y\right)\right)}{\mathsf{neg}\left(\left(x \cdot 2\right) \cdot y\right)}\right)}}^{-1} \]

      5. neg-mul-1 N/A

         \[\leadsto {\left(\frac{\color{blue}{-1 \cdot \left(x - y\right)}}{\mathsf{neg}\left(\left(x \cdot 2\right) \cdot y\right)}\right)}^{-1} \]

      6. lift-*.f64 N/A

         \[\leadsto {\left(\frac{-1 \cdot \left(x - y\right)}{\mathsf{neg}\left(\color{blue}{\left(x \cdot 2\right) \cdot y}\right)}\right)}^{-1} \]

      7. distribute-lft-neg-in N/A

         \[\leadsto {\left(\frac{-1 \cdot \left(x - y\right)}{\color{blue}{\left(\mathsf{neg}\left(x \cdot 2\right)\right) \cdot y}}\right)}^{-1} \]

      8. times-frac N/A

         \[\leadsto {\color{blue}{\left(\frac{-1}{\mathsf{neg}\left(x \cdot 2\right)} \cdot \frac{x - y}{y}\right)}}^{-1} \]

      9. unpow-prod-down N/A

         \[\leadsto \color{blue}{{\left(\frac{-1}{\mathsf{neg}\left(x \cdot 2\right)}\right)}^{-1} \cdot {\left(\frac{x - y}{y}\right)}^{-1}} \]

      10. metadata-eval N/A

          \[\leadsto {\left(\frac{\color{blue}{\mathsf{neg}\left(1\right)}}{\mathsf{neg}\left(x \cdot 2\right)}\right)}^{-1} \cdot {\left(\frac{x - y}{y}\right)}^{-1} \]

      11. frac-2neg N/A

          \[\leadsto {\color{blue}{\left(\frac{1}{x \cdot 2}\right)}}^{-1} \cdot {\left(\frac{x - y}{y}\right)}^{-1} \]

      12. inv-pow N/A

          \[\leadsto {\left(\frac{1}{x \cdot 2}\right)}^{-1} \cdot \color{blue}{\frac{1}{\frac{x - y}{y}}} \]

      13. clear-num N/A

          \[\leadsto {\left(\frac{1}{x \cdot 2}\right)}^{-1} \cdot \color{blue}{\frac{y}{x - y}} \]

      14. lower-*.f64 N/A

          \[\leadsto \color{blue}{{\left(\frac{1}{x \cdot 2}\right)}^{-1} \cdot \frac{y}{x - y}} \]

      15. lower-pow.f64 N/A

          \[\leadsto \color{blue}{{\left(\frac{1}{x \cdot 2}\right)}^{-1}} \cdot \frac{y}{x - y} \]

      16. inv-pow N/A

          \[\leadsto {\color{blue}{\left({\left(x \cdot 2\right)}^{-1}\right)}}^{-1} \cdot \frac{y}{x - y} \]

      17. lower-pow.f64 N/A

          \[\leadsto {\color{blue}{\left({\left(x \cdot 2\right)}^{-1}\right)}}^{-1} \cdot \frac{y}{x - y} \]

      18. lift-*.f64 N/A

          \[\leadsto {\left({\color{blue}{\left(x \cdot 2\right)}}^{-1}\right)}^{-1} \cdot \frac{y}{x - y} \]

      19. *-commutative N/A

          \[\leadsto {\left({\color{blue}{\left(2 \cdot x\right)}}^{-1}\right)}^{-1} \cdot \frac{y}{x - y} \]

      20. lower-*.f64 N/A

          \[\leadsto {\left({\color{blue}{\left(2 \cdot x\right)}}^{-1}\right)}^{-1} \cdot \frac{y}{x - y} \]

      21. lower-/.f64 99.8

          \[\leadsto {\left({\left(2 \cdot x\right)}^{-1}\right)}^{-1} \cdot \color{blue}{\frac{y}{x - y}} \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{{\left({\left(2 \cdot x\right)}^{-1}\right)}^{-1} \cdot \frac{y}{x - y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-130}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{x - y} \cdot {\left({\left(2 \cdot x\right)}^{-1}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x - y} \cdot \left(2 \cdot y\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{-157}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-134}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, -2, -2\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ x (- x y)) (* 2.0 y))))
   (if (<= x -1.05e-157)
     t_0
     (if (<= x 6.5e-134) (* (fma (/ x y) -2.0 -2.0) x) t_0))))

C

double code(double x, double y) {
	double t_0 = (x / (x - y)) * (2.0 * y);
	double tmp;
	if (x <= -1.05e-157) {
		tmp = t_0;
	} else if (x <= 6.5e-134) {
		tmp = fma((x / y), -2.0, -2.0) * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(x / Float64(x - y)) * Float64(2.0 * y))
	tmp = 0.0
	if (x <= -1.05e-157)
		tmp = t_0;
	elseif (x <= 6.5e-134)
		tmp = Float64(fma(Float64(x / y), -2.0, -2.0) * x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision] * N[(2.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e-157], t$95$0, If[LessEqual[x, 6.5e-134], N[(N[(N[(x / y), $MachinePrecision] * -2.0 + -2.0), $MachinePrecision] * x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e-157 or 6.4999999999999998e-134 < x

   1. Initial program 82.5%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 99.4

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

   4. Applied rewrites 99.4%

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

   if -1.05e-157 < x < 6.4999999999999998e-134

   1. Initial program 72.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(-2 \cdot \frac{x}{y} - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

         \[\leadsto \color{blue}{\left(-2 \cdot \frac{x}{y} + \left(\mathsf{neg}\left(2\right)\right)\right)} \cdot x \]

      4. *-commutative N/A

         \[\leadsto \left(\color{blue}{\frac{x}{y} \cdot -2} + \left(\mathsf{neg}\left(2\right)\right)\right) \cdot x \]

      5. metadata-eval N/A

         \[\leadsto \left(\frac{x}{y} \cdot -2 + \color{blue}{-2}\right) \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, -2, -2\right)} \cdot x \]

      7. lower-/.f64 96.4

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{x}{y}}, -2, -2\right) \cdot x \]

   5. Applied rewrites 96.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, -2, -2\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-134}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, -2, -2\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y} \cdot \left(2 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-21}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 0.0035:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, -2, -2\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9e-21)
   (* 2.0 y)
   (if (<= x 0.0035) (* (fma (/ x y) -2.0 -2.0) x) (* 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9e-21) {
		tmp = 2.0 * y;
	} else if (x <= 0.0035) {
		tmp = fma((x / y), -2.0, -2.0) * x;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9e-21)
		tmp = Float64(2.0 * y);
	elseif (x <= 0.0035)
		tmp = Float64(fma(Float64(x / y), -2.0, -2.0) * x);
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9e-21], N[(2.0 * y), $MachinePrecision], If[LessEqual[x, 0.0035], N[(N[(N[(x / y), $MachinePrecision] * -2.0 + -2.0), $MachinePrecision] * x), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.99999999999999936e-21 or 0.00350000000000000007 < x

   1. Initial program 81.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 77.8

         \[\leadsto \color{blue}{2 \cdot y} \]

   5. Applied rewrites 77.8%

      \[\leadsto \color{blue}{2 \cdot y} \]

   if -8.99999999999999936e-21 < x < 0.00350000000000000007

   1. Initial program 79.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(-2 \cdot \frac{x}{y} - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

         \[\leadsto \color{blue}{\left(-2 \cdot \frac{x}{y} + \left(\mathsf{neg}\left(2\right)\right)\right)} \cdot x \]

      4. *-commutative N/A

         \[\leadsto \left(\color{blue}{\frac{x}{y} \cdot -2} + \left(\mathsf{neg}\left(2\right)\right)\right) \cdot x \]

      5. metadata-eval N/A

         \[\leadsto \left(\frac{x}{y} \cdot -2 + \color{blue}{-2}\right) \cdot x \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, -2, -2\right)} \cdot x \]

      7. lower-/.f64 78.7

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{x}{y}}, -2, -2\right) \cdot x \]

   5. Applied rewrites 78.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, -2, -2\right) \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 75.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-20}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 0.004:\\ \;\;\;\;-2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1e-20) (* 2.0 y) (if (<= x 0.004) (* -2.0 x) (* 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1e-20) {
		tmp = 2.0 * y;
	} else if (x <= 0.004) {
		tmp = -2.0 * x;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1d-20)) then
        tmp = 2.0d0 * y
    else if (x <= 0.004d0) then
        tmp = (-2.0d0) * x
    else
        tmp = 2.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1e-20) {
		tmp = 2.0 * y;
	} else if (x <= 0.004) {
		tmp = -2.0 * x;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1e-20:
		tmp = 2.0 * y
	elif x <= 0.004:
		tmp = -2.0 * x
	else:
		tmp = 2.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1e-20)
		tmp = Float64(2.0 * y);
	elseif (x <= 0.004)
		tmp = Float64(-2.0 * x);
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1e-20)
		tmp = 2.0 * y;
	elseif (x <= 0.004)
		tmp = -2.0 * x;
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1e-20], N[(2.0 * y), $MachinePrecision], If[LessEqual[x, 0.004], N[(-2.0 * x), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.99999999999999945e-21 or 0.0040000000000000001 < x

   1. Initial program 81.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 77.8

         \[\leadsto \color{blue}{2 \cdot y} \]

   5. Applied rewrites 77.8%

      \[\leadsto \color{blue}{2 \cdot y} \]

   if -9.99999999999999945e-21 < x < 0.0040000000000000001

   1. Initial program 79.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 78.5

         \[\leadsto \color{blue}{-2 \cdot x} \]

   5. Applied rewrites 78.5%

      \[\leadsto \color{blue}{-2 \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 50.4% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ -2 \cdot x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.0%

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

3. Taylor expanded in x around 0

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

   1. lower-*.f64 51.0

      \[\leadsto \color{blue}{-2 \cdot x} \]

5. Applied rewrites 51.0%

   \[\leadsto \color{blue}{-2 \cdot x} \]
6. Add Preprocessing

Developer Target 1: 99.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{if}\;x < -1.7210442634149447 \cdot 10^{+81}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 83645045635564430:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ (* 2.0 x) (- x y)) y)))
   (if (< x -1.7210442634149447e+81)
     t_0
     (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) t_0))))

C

double code(double x, double y) {
	double t_0 = ((2.0 * x) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((2.0d0 * x) / (x - y)) * y
    if (x < (-1.7210442634149447d+81)) then
        tmp = t_0
    else if (x < 83645045635564430.0d0) then
        tmp = (x * 2.0d0) / ((x - y) / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((2.0 * x) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((2.0 * x) / (x - y)) * y
	tmp = 0
	if x < -1.7210442634149447e+81:
		tmp = t_0
	elif x < 83645045635564430.0:
		tmp = (x * 2.0) / ((x - y) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(2.0 * x) / Float64(x - y)) * y)
	tmp = 0.0
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((2.0 * x) / (x - y)) * y;
	tmp = 0.0;
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = (x * 2.0) / ((x - y) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(2.0 * x), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[Less[x, -1.7210442634149447e+81], t$95$0, If[Less[x, 83645045635564430.0], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024294 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -1721044263414944700000000000000000000000000000000000000000000000000000000000000000) (* (/ (* 2 x) (- x y)) y) (if (< x 83645045635564430) (/ (* x 2) (/ (- x y) y)) (* (/ (* 2 x) (- x y)) y))))

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