Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3

Percentage Accurate: 77.8% → 100.0%

Time: 6.6s

Alternatives: 7

Speedup: 1.5×

Specification

Math

\[\begin{array}{l} \\ x + \left(1 - x\right) \cdot \left(1 - y\right) \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((1.0d0 - x) * (1.0d0 - y))
end function

Java

public static double code(double x, double y) {
	return x + ((1.0 - x) * (1.0 - y));
}

Python

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

Julia

function code(x, y)
	return Float64(x + Float64(Float64(1.0 - x) * Float64(1.0 - y)))
end

MATLAB

function tmp = code(x, y)
	tmp = x + ((1.0 - x) * (1.0 - y));
end

Wolfram

code[x_, y_] := N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 77.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(1 - x\right) \cdot \left(1 - y\right) \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((1.0d0 - x) * (1.0d0 - y))
end function

Java

public static double code(double x, double y) {
	return x + ((1.0 - x) * (1.0 - y));
}

Python

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

Julia

function code(x, y)
	return Float64(x + Float64(Float64(1.0 - x) * Float64(1.0 - y)))
end

MATLAB

function tmp = code(x, y)
	tmp = x + ((1.0 - x) * (1.0 - y));
end

Wolfram

code[x_, y_] := N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x - 1, y, 1\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma (- x 1.0) y 1.0))

C

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

Julia

function code(x, y)
	return fma(Float64(x - 1.0), y, 1.0)
end

Wolfram

code[x_, y_] := N[(N[(x - 1.0), $MachinePrecision] * y + 1.0), $MachinePrecision]

Derivation

1. Initial program 71.1%

   \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1 + -1 \cdot \left(y \cdot \left(1 - x\right)\right)} \]
4. Step-by-step derivation

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. associate-*r* N/A

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

   4. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(1 - x\right), y, 1\right)} \]

   5. mul-1-neg N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(1 - x\right)\right)}, y, 1\right) \]

   6. sub-neg N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(1 + \left(\mathsf{neg}\left(x\right)\right)\right)}\right), y, 1\right) \]

   7. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + 1\right)}\right), y, 1\right) \]

   8. distribute-neg-in N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \left(\mathsf{neg}\left(1\right)\right)}, y, 1\right) \]

   9. remove-double-neg N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{x} + \left(\mathsf{neg}\left(1\right)\right), y, 1\right) \]

   10. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{x - 1}, y, 1\right) \]

   11. lower--.f64 100.0

       \[\leadsto \mathsf{fma}\left(\color{blue}{x - 1}, y, 1\right) \]

5. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x - 1, y, 1\right)} \]
6. Add Preprocessing

Alternative 2: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-31}:\\ \;\;\;\;\left(x - 1\right) \cdot y\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-83}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.2e-31) (* (- x 1.0) y) (if (<= y 2.75e-83) 1.0 (fma y x (- y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.2e-31) {
		tmp = (x - 1.0) * y;
	} else if (y <= 2.75e-83) {
		tmp = 1.0;
	} else {
		tmp = fma(y, x, -y);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.2e-31)
		tmp = Float64(Float64(x - 1.0) * y);
	elseif (y <= 2.75e-83)
		tmp = 1.0;
	else
		tmp = fma(y, x, Float64(-y));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.2e-31], N[(N[(x - 1.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 2.75e-83], 1.0, N[(y * x + (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e-31

   1. Initial program 91.5%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(1 - x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(1 + \left(\mathsf{neg}\left(x\right)\right)\right)}\right)\right) \cdot y \]

      6. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + 1\right)}\right)\right) \cdot y \]

      7. distribute-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \left(\mathsf{neg}\left(1\right)\right)\right)} \cdot y \]

      8. remove-double-neg N/A

         \[\leadsto \left(\color{blue}{x} + \left(\mathsf{neg}\left(1\right)\right)\right) \cdot y \]

      9. sub-neg N/A

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

      10. lower--.f64 94.9

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

   5. Applied rewrites 94.9%

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

   if -1.2e-31 < y < 2.74999999999999982e-83

   1. Initial program 44.7%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 77.2%

      \[\leadsto \color{blue}{1} \]

   if 2.74999999999999982e-83 < y

   1. Initial program 85.2%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(1 - x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(1 + \left(\mathsf{neg}\left(x\right)\right)\right)}\right)\right) \cdot y \]

      6. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + 1\right)}\right)\right) \cdot y \]

      7. distribute-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \left(\mathsf{neg}\left(1\right)\right)\right)} \cdot y \]

      8. remove-double-neg N/A

         \[\leadsto \left(\color{blue}{x} + \left(\mathsf{neg}\left(1\right)\right)\right) \cdot y \]

      9. sub-neg N/A

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

      10. lower--.f64 89.9

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

   5. Applied rewrites 89.9%

      \[\leadsto \color{blue}{\left(x - 1\right) \cdot y} \]
   6. Step-by-step derivation

   7. Applied rewrites 90.0%

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

Alternative 3: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 1\right) \cdot y\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{-31}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-83}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (- x 1.0) y)))
   (if (<= y -1.2e-31) t_0 (if (<= y 2.75e-83) 1.0 t_0))))

C

double code(double x, double y) {
	double t_0 = (x - 1.0) * y;
	double tmp;
	if (y <= -1.2e-31) {
		tmp = t_0;
	} else if (y <= 2.75e-83) {
		tmp = 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 - 1.0d0) * y
    if (y <= (-1.2d-31)) then
        tmp = t_0
    else if (y <= 2.75d-83) then
        tmp = 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 - 1.0) * y;
	double tmp;
	if (y <= -1.2e-31) {
		tmp = t_0;
	} else if (y <= 2.75e-83) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - 1.0) * y
	tmp = 0
	if y <= -1.2e-31:
		tmp = t_0
	elif y <= 2.75e-83:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - 1.0) * y)
	tmp = 0.0
	if (y <= -1.2e-31)
		tmp = t_0;
	elseif (y <= 2.75e-83)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - 1.0) * y;
	tmp = 0.0;
	if (y <= -1.2e-31)
		tmp = t_0;
	elseif (y <= 2.75e-83)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - 1.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.2e-31], t$95$0, If[LessEqual[y, 2.75e-83], 1.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e-31 or 2.74999999999999982e-83 < y

   1. Initial program 88.0%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(1 - x\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(1 + \left(\mathsf{neg}\left(x\right)\right)\right)}\right)\right) \cdot y \]

      6. +-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + 1\right)}\right)\right) \cdot y \]

      7. distribute-neg-in N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \left(\mathsf{neg}\left(1\right)\right)\right)} \cdot y \]

      8. remove-double-neg N/A

         \[\leadsto \left(\color{blue}{x} + \left(\mathsf{neg}\left(1\right)\right)\right) \cdot y \]

      9. sub-neg N/A

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

      10. lower--.f64 92.1

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

   5. Applied rewrites 92.1%

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

   if -1.2e-31 < y < 2.74999999999999982e-83

   1. Initial program 44.7%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 77.2%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+75}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+112}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.2e+75) (* y x) (if (<= x 2.9e+112) (- 1.0 y) (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.2e+75) {
		tmp = y * x;
	} else if (x <= 2.9e+112) {
		tmp = 1.0 - y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.2d+75)) then
        tmp = y * x
    else if (x <= 2.9d+112) then
        tmp = 1.0d0 - y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.2e+75) {
		tmp = y * x;
	} else if (x <= 2.9e+112) {
		tmp = 1.0 - y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.2e+75:
		tmp = y * x
	elif x <= 2.9e+112:
		tmp = 1.0 - y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.2e+75)
		tmp = Float64(y * x);
	elseif (x <= 2.9e+112)
		tmp = Float64(1.0 - y);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.2e+75)
		tmp = y * x;
	elseif (x <= 2.9e+112)
		tmp = 1.0 - y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.2e+75], N[(y * x), $MachinePrecision], If[LessEqual[x, 2.9e+112], N[(1.0 - y), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2000000000000002e75 or 2.9000000000000002e112 < x

   1. Initial program 49.1%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \left(1 - y\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. sub-neg N/A

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

      4. associate--r+ N/A

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

      5. metadata-eval N/A

         \[\leadsto x \cdot \left(\color{blue}{0} - \left(\mathsf{neg}\left(y\right)\right)\right) \]

      6. neg-sub0 N/A

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

      7. remove-double-neg N/A

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

      8. lower-*.f64 85.6

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

   5. Applied rewrites 85.6%

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

   if -6.2000000000000002e75 < x < 2.9000000000000002e112

   1. Initial program 84.0%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 - y} \]
   4. Step-by-step derivation

      1. lower--.f64 86.1

         \[\leadsto \color{blue}{1 - y} \]

   5. Applied rewrites 86.1%

      \[\leadsto \color{blue}{1 - y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+75}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+112}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (- y) (if (<= y 1.0) 1.0 (- y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = -y
    else if (y <= 1.0d0) then
        tmp = 1.0d0
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = -y
	elif y <= 1.0:
		tmp = 1.0
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(-y);
	elseif (y <= 1.0)
		tmp = 1.0;
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = 1.0;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], (-y), If[LessEqual[y, 1.0], 1.0, (-y)]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 - y} \]
   4. Step-by-step derivation

      1. lower--.f64 52.9

         \[\leadsto \color{blue}{1 - y} \]

   5. Applied rewrites 52.9%

      \[\leadsto \color{blue}{1 - y} \]

   6. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \color{blue}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 52.5%

      \[\leadsto -y \]

   if -1 < y < 1

   1. Initial program 43.4%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 66.6%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 63.1% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ 1 - y \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 - y
end function

Java

public static double code(double x, double y) {
	return 1.0 - y;
}

Python

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

Julia

function code(x, y)
	return Float64(1.0 - y)
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 - y;
end

Wolfram

code[x_, y_] := N[(1.0 - y), $MachinePrecision]

Derivation

1. Initial program 71.1%

   \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1 - y} \]
4. Step-by-step derivation

   1. lower--.f64 60.4

      \[\leadsto \color{blue}{1 - y} \]

5. Applied rewrites 60.4%

   \[\leadsto \color{blue}{1 - y} \]
6. Add Preprocessing

Alternative 7: 39.0% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 71.1%

   \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 35.3%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ y \cdot x - \left(y - 1\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* y x) (- y 1.0)))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y * x) - (y - 1.0d0)
end function

Java

public static double code(double x, double y) {
	return (y * x) - (y - 1.0);
}

Python

def code(x, y):
	return (y * x) - (y - 1.0)

Julia

function code(x, y)
	return Float64(Float64(y * x) - Float64(y - 1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (y * x) - (y - 1.0);
end

Wolfram

code[x_, y_] := N[(N[(y * x), $MachinePrecision] - N[(y - 1.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024267 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* y x) (- y 1)))

  (+ x (* (- 1.0 x) (- 1.0 y))))