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

Percentage Accurate: 77.5% → 100.0%

Time: 3.7s

Alternatives: 7

Speedup: 1.3×

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: 77.5% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 73.6%

   \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
2. Step-by-step derivation

   1. sub-neg 73.6%

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

   2. distribute-rgt-in 73.6%

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

   3. *-lft-identity 73.6%

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

   4. associate-+r+ 86.6%

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

   5. +-commutative 86.6%

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

   6. sub-neg 86.6%

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

   7. associate-+l+ 100.0%

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

   8. neg-mul-1 100.0%

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

   9. distribute-lft1-in 100.0%

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

   10. metadata-eval 100.0%

       \[\leadsto \left(1 + \color{blue}{0} \cdot x\right) + \left(-y\right) \cdot \left(1 - x\right) \]

   11. metadata-eval 100.0%

       \[\leadsto \left(1 + \color{blue}{\left(0 \cdot -1\right)} \cdot x\right) + \left(-y\right) \cdot \left(1 - x\right) \]

   12. associate-*r* 100.0%

       \[\leadsto \left(1 + \color{blue}{0 \cdot \left(-1 \cdot x\right)}\right) + \left(-y\right) \cdot \left(1 - x\right) \]

   13. neg-mul-1 100.0%

       \[\leadsto \left(1 + 0 \cdot \color{blue}{\left(-x\right)}\right) + \left(-y\right) \cdot \left(1 - x\right) \]

   14. mul0-lft 100.0%

       \[\leadsto \left(1 + \color{blue}{0}\right) + \left(-y\right) \cdot \left(1 - x\right) \]

   15. metadata-eval 100.0%

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

   16. sub-neg 100.0%

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

   17. distribute-rgt-in 100.0%

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

   18. *-lft-identity 100.0%

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

   19. associate-+r+ 100.0%

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

   20. sub-neg 100.0%

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

   21. +-commutative 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 60.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+270}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{+209}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+185}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-38}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-147}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+69}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5e+270)
   (- y)
   (if (<= y -2.35e+209)
     (* x y)
     (if (<= y -1.12e+185)
       (- y)
       (if (<= y -1.02e-38)
         (* x y)
         (if (<= y 1.22e-147) 1.0 (if (<= y 1.4e+69) (* x y) (- y))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e+270) {
		tmp = -y;
	} else if (y <= -2.35e+209) {
		tmp = x * y;
	} else if (y <= -1.12e+185) {
		tmp = -y;
	} else if (y <= -1.02e-38) {
		tmp = x * y;
	} else if (y <= 1.22e-147) {
		tmp = 1.0;
	} else if (y <= 1.4e+69) {
		tmp = x * y;
	} 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 <= (-5d+270)) then
        tmp = -y
    else if (y <= (-2.35d+209)) then
        tmp = x * y
    else if (y <= (-1.12d+185)) then
        tmp = -y
    else if (y <= (-1.02d-38)) then
        tmp = x * y
    else if (y <= 1.22d-147) then
        tmp = 1.0d0
    else if (y <= 1.4d+69) then
        tmp = x * y
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5e+270) {
		tmp = -y;
	} else if (y <= -2.35e+209) {
		tmp = x * y;
	} else if (y <= -1.12e+185) {
		tmp = -y;
	} else if (y <= -1.02e-38) {
		tmp = x * y;
	} else if (y <= 1.22e-147) {
		tmp = 1.0;
	} else if (y <= 1.4e+69) {
		tmp = x * y;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e+270:
		tmp = -y
	elif y <= -2.35e+209:
		tmp = x * y
	elif y <= -1.12e+185:
		tmp = -y
	elif y <= -1.02e-38:
		tmp = x * y
	elif y <= 1.22e-147:
		tmp = 1.0
	elif y <= 1.4e+69:
		tmp = x * y
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e+270)
		tmp = Float64(-y);
	elseif (y <= -2.35e+209)
		tmp = Float64(x * y);
	elseif (y <= -1.12e+185)
		tmp = Float64(-y);
	elseif (y <= -1.02e-38)
		tmp = Float64(x * y);
	elseif (y <= 1.22e-147)
		tmp = 1.0;
	elseif (y <= 1.4e+69)
		tmp = Float64(x * y);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e+270)
		tmp = -y;
	elseif (y <= -2.35e+209)
		tmp = x * y;
	elseif (y <= -1.12e+185)
		tmp = -y;
	elseif (y <= -1.02e-38)
		tmp = x * y;
	elseif (y <= 1.22e-147)
		tmp = 1.0;
	elseif (y <= 1.4e+69)
		tmp = x * y;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e+270], (-y), If[LessEqual[y, -2.35e+209], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.12e+185], (-y), If[LessEqual[y, -1.02e-38], N[(x * y), $MachinePrecision], If[LessEqual[y, 1.22e-147], 1.0, If[LessEqual[y, 1.4e+69], N[(x * y), $MachinePrecision], (-y)]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.99999999999999976e270 or -2.35e209 < y < -1.11999999999999996e185 or 1.39999999999999991e69 < y

   1. Initial program 100.0%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. remove-double-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 63.7%

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

      1. neg-mul-1 63.7%

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

   7. Simplified 63.7%

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

   if -4.99999999999999976e270 < y < -2.35e209 or -1.11999999999999996e185 < y < -1.01999999999999998e-38 or 1.21999999999999995e-147 < y < 1.39999999999999991e69

   1. Initial program 78.9%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in x around inf 43.1%

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

      1. mul-1-neg 43.1%

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

      2. unsub-neg 43.1%

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

      3. sub-neg 43.1%

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

      4. associate--r+ 63.4%

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

      5. metadata-eval 63.4%

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

      6. neg-sub0 63.4%

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

      7. remove-double-neg 63.4%

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

   4. Simplified 63.4%

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

   if -1.01999999999999998e-38 < y < 1.21999999999999995e-147

   1. Initial program 48.8%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around 0 84.4%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+270}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{+209}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+185}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-38}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-147}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+69}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 3: 84.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + -1\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-147}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-54}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 420:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (+ x -1.0))))
   (if (<= y -2.5e-40)
     t_0
     (if (<= y 1.22e-147)
       (- 1.0 y)
       (if (<= y 2.7e-54) (* x y) (if (<= y 420.0) (- 1.0 y) t_0))))))

C

double code(double x, double y) {
	double t_0 = y * (x + -1.0);
	double tmp;
	if (y <= -2.5e-40) {
		tmp = t_0;
	} else if (y <= 1.22e-147) {
		tmp = 1.0 - y;
	} else if (y <= 2.7e-54) {
		tmp = x * y;
	} else if (y <= 420.0) {
		tmp = 1.0 - 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 = y * (x + (-1.0d0))
    if (y <= (-2.5d-40)) then
        tmp = t_0
    else if (y <= 1.22d-147) then
        tmp = 1.0d0 - y
    else if (y <= 2.7d-54) then
        tmp = x * y
    else if (y <= 420.0d0) then
        tmp = 1.0d0 - y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y * (x + -1.0);
	double tmp;
	if (y <= -2.5e-40) {
		tmp = t_0;
	} else if (y <= 1.22e-147) {
		tmp = 1.0 - y;
	} else if (y <= 2.7e-54) {
		tmp = x * y;
	} else if (y <= 420.0) {
		tmp = 1.0 - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * (x + -1.0)
	tmp = 0
	if y <= -2.5e-40:
		tmp = t_0
	elif y <= 1.22e-147:
		tmp = 1.0 - y
	elif y <= 2.7e-54:
		tmp = x * y
	elif y <= 420.0:
		tmp = 1.0 - y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(x + -1.0))
	tmp = 0.0
	if (y <= -2.5e-40)
		tmp = t_0;
	elseif (y <= 1.22e-147)
		tmp = Float64(1.0 - y);
	elseif (y <= 2.7e-54)
		tmp = Float64(x * y);
	elseif (y <= 420.0)
		tmp = Float64(1.0 - y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * (x + -1.0);
	tmp = 0.0;
	if (y <= -2.5e-40)
		tmp = t_0;
	elseif (y <= 1.22e-147)
		tmp = 1.0 - y;
	elseif (y <= 2.7e-54)
		tmp = x * y;
	elseif (y <= 420.0)
		tmp = 1.0 - y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e-40], t$95$0, If[LessEqual[y, 1.22e-147], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, 2.7e-54], N[(x * y), $MachinePrecision], If[LessEqual[y, 420.0], N[(1.0 - y), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999982e-40 or 420 < y

   1. Initial program 96.2%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around inf 95.6%

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

      1. mul-1-neg 95.6%

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

      2. distribute-rgt-neg-in 95.6%

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

      3. sub-neg 95.6%

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

      4. distribute-neg-in 95.6%

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

      5. metadata-eval 95.6%

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

      6. remove-double-neg 95.6%

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

   4. Simplified 95.6%

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

   if -2.49999999999999982e-40 < y < 1.21999999999999995e-147 or 2.70000000000000026e-54 < y < 420

   1. Initial program 52.1%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in x around 0 82.5%

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

   if 1.21999999999999995e-147 < y < 2.70000000000000026e-54

   1. Initial program 15.6%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in x around inf 2.7%

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

      1. mul-1-neg 2.7%

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

      2. unsub-neg 2.7%

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

      3. sub-neg 2.7%

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

      4. associate--r+ 82.8%

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

      5. metadata-eval 82.8%

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

      6. neg-sub0 82.8%

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

      7. remove-double-neg 82.8%

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

   4. Simplified 82.8%

      \[\leadsto \color{blue}{y \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-147}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-54}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 420:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 4: 85.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -58000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+121}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -58000000000.0) (* x y) (if (<= x 7.5e+121) (- 1.0 y) (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -58000000000.0) {
		tmp = x * y;
	} else if (x <= 7.5e+121) {
		tmp = 1.0 - y;
	} else {
		tmp = x * 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 <= (-58000000000.0d0)) then
        tmp = x * y
    else if (x <= 7.5d+121) then
        tmp = 1.0d0 - y
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -58000000000.0) {
		tmp = x * y;
	} else if (x <= 7.5e+121) {
		tmp = 1.0 - y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -58000000000.0:
		tmp = x * y
	elif x <= 7.5e+121:
		tmp = 1.0 - y
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -58000000000.0)
		tmp = Float64(x * y);
	elseif (x <= 7.5e+121)
		tmp = Float64(1.0 - y);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -58000000000.0)
		tmp = x * y;
	elseif (x <= 7.5e+121)
		tmp = 1.0 - y;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -58000000000.0], N[(x * y), $MachinePrecision], If[LessEqual[x, 7.5e+121], N[(1.0 - y), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.8e10 or 7.49999999999999965e121 < x

   1. Initial program 52.3%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in x around inf 52.1%

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

      1. mul-1-neg 52.1%

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

      2. unsub-neg 52.1%

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

      3. sub-neg 52.1%

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

      4. associate--r+ 79.2%

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

      5. metadata-eval 79.2%

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

      6. neg-sub0 79.2%

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

      7. remove-double-neg 79.2%

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

   4. Simplified 79.2%

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

   if -5.8e10 < x < 7.49999999999999965e121

   1. Initial program 89.9%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in x around 0 90.6%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -58000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+121}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.6%

   \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

2. Taylor expanded in x around -inf 100.0%

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

3. Final simplification 100.0%

   \[\leadsto \left(1 + x \cdot y\right) - y \]

Alternative 6: 61.9% accurate, 1.5× 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. Taylor expanded in y around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. distribute-rgt-neg-in 98.9%

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

      3. sub-neg 98.9%

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

      4. distribute-neg-in 98.9%

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

      5. metadata-eval 98.9%

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

      6. remove-double-neg 98.9%

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

   4. Simplified 98.9%

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

   5. Taylor expanded in x around 0 49.3%

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

      1. neg-mul-1 49.3%

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

   7. Simplified 49.3%

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

   if -1 < y < 1

   1. Initial program 48.0%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around 0 69.5%

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

4. Final simplification 59.6%

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

Alternative 7: 38.2% accurate, 9.0× 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 73.6%

   \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

2. Taylor expanded in y around 0 36.6%

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

3. Final simplification 36.6%

   \[\leadsto 1 \]

Developer target: 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 2023230 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- (* y x) (- y 1.0))

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