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

Percentage Accurate: 77.6% → 100.0%

Time: 7.6s

Alternatives: 6

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: 77.6% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 81.2%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. mul-1-neg N/A

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

   6. unsub-neg N/A

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

   7. sub-neg N/A

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

   8. associate--r+ N/A

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

   9. metadata-eval N/A

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

   10. neg-sub0 N/A

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

   11. cancel-sign-sub-inv N/A

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

   12. associate--r+ N/A

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

   13. +-commutative N/A

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

   14. distribute-lft-neg-out N/A

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

   15. distribute-rgt-neg-out N/A

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

   16. *-rgt-identity N/A

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

   17. distribute-lft-in N/A

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

   18. +-commutative N/A

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

   19. sub-neg N/A

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

   20. unsub-neg N/A

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

   21. mul-1-neg N/A

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

   22. +-commutative N/A

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

5. Simplified 100.0%

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

Alternative 2: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -76000:\\ \;\;\;\;\mathsf{fma}\left(y, x, 1\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-8}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -76000.0) (fma y x 1.0) (if (<= x 9.2e-8) (- 1.0 y) (fma y x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -76000.0) {
		tmp = fma(y, x, 1.0);
	} else if (x <= 9.2e-8) {
		tmp = 1.0 - y;
	} else {
		tmp = fma(y, x, 1.0);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -76000.0)
		tmp = fma(y, x, 1.0);
	elseif (x <= 9.2e-8)
		tmp = Float64(1.0 - y);
	else
		tmp = fma(y, x, 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -76000.0], N[(y * x + 1.0), $MachinePrecision], If[LessEqual[x, 9.2e-8], N[(1.0 - y), $MachinePrecision], N[(y * x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -76000 or 9.2000000000000003e-8 < x

   1. Initial program 62.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. sub-neg N/A

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

      8. associate--r+ N/A

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

      9. metadata-eval N/A

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

      10. neg-sub0 N/A

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

      11. cancel-sign-sub-inv N/A

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

      12. associate--r+ N/A

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

      13. +-commutative N/A

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

      14. distribute-lft-neg-out N/A

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

      15. distribute-rgt-neg-out N/A

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

      16. *-rgt-identity N/A

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

      17. distribute-lft-in N/A

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

      18. +-commutative N/A

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

      19. sub-neg N/A

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

      20. unsub-neg N/A

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

      21. mul-1-neg N/A

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

      22. +-commutative N/A

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma.f64}\left(y, \color{blue}{x}, 1\right) \]
   7. Step-by-step derivation

   8. Simplified 99.2%

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

   if -76000 < x < 9.2000000000000003e-8

   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. --lowering--.f64 99.8%

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{y}\right) \]

   5. Simplified 99.8%

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

Alternative 3: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.45 \cdot 10^{+21}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 1660000000000:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.45e+21) (* y x) (if (<= x 1660000000000.0) (- 1.0 y) (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.45e+21) {
		tmp = y * x;
	} else if (x <= 1660000000000.0) {
		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 <= (-3.45d+21)) then
        tmp = y * x
    else if (x <= 1660000000000.0d0) 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 <= -3.45e+21) {
		tmp = y * x;
	} else if (x <= 1660000000000.0) {
		tmp = 1.0 - y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.45e+21:
		tmp = y * x
	elif x <= 1660000000000.0:
		tmp = 1.0 - y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.45e+21)
		tmp = Float64(y * x);
	elseif (x <= 1660000000000.0)
		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 <= -3.45e+21)
		tmp = y * x;
	elseif (x <= 1660000000000.0)
		tmp = 1.0 - y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.45e+21], N[(y * x), $MachinePrecision], If[LessEqual[x, 1660000000000.0], N[(1.0 - y), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.45e21 or 1.66e12 < x

   1. Initial program 60.3%

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

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

      2. unsub-neg N/A

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

      3. sub-neg N/A

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

      4. associate--r+ N/A

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

      5. metadata-eval N/A

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

      6. neg-sub0 N/A

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

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

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

      8. distribute-lft-neg-out N/A

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

      9. +-rgt-identity N/A

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

      10. *-commutative N/A

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

      11. distribute-lft-neg-out N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. remove-double-neg N/A

          \[\leadsto y \cdot x + 0 \]

      14. accelerator-lowering-fma.f64 83.1%

          \[\leadsto \mathsf{fma.f64}\left(y, \color{blue}{x}, 0\right) \]

   5. Simplified 83.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-lowering-*.f64 83.1%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{x}\right) \]

   7. Applied egg-rr 83.1%

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

   if -3.45e21 < x < 1.66e12

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0

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

      1. --lowering--.f64 98.5%

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{y}\right) \]

   5. Simplified 98.5%

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

Alternative 4: 61.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8600000:\\ \;\;\;\;0 - y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8600000.0) (- 0.0 y) (if (<= y 1.0) 1.0 (- 0.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8600000.0) {
		tmp = 0.0 - y;
	} else if (y <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = 0.0 - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-8600000.0d0)) then
        tmp = 0.0d0 - y
    else if (y <= 1.0d0) then
        tmp = 1.0d0
    else
        tmp = 0.0d0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -8600000.0) {
		tmp = 0.0 - y;
	} else if (y <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = 0.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8600000.0:
		tmp = 0.0 - y
	elif y <= 1.0:
		tmp = 1.0
	else:
		tmp = 0.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8600000.0)
		tmp = Float64(0.0 - y);
	elseif (y <= 1.0)
		tmp = 1.0;
	else
		tmp = Float64(0.0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -8600000.0)
		tmp = 0.0 - y;
	elseif (y <= 1.0)
		tmp = 1.0;
	else
		tmp = 0.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8600000.0], N[(0.0 - y), $MachinePrecision], If[LessEqual[y, 1.0], 1.0, N[(0.0 - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.6e6 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. --lowering--.f64 48.7%

         \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{y}\right) \]

   5. Simplified 48.7%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{y} \]

      3. --lowering--.f64 48.2%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{y}\right) \]

   8. Simplified 48.2%

      \[\leadsto \color{blue}{0 - y} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(y\right) \]

      2. neg-lowering-neg.f64 48.2%

         \[\leadsto \mathsf{neg.f64}\left(y\right) \]

   10. Applied egg-rr 48.2%

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

   if -8.6e6 < y < 1

   1. Initial program 61.7%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 73.7%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8600000:\\ \;\;\;\;0 - y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0 - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.4% 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 81.2%

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

3. Taylor expanded in x around 0

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

   1. --lowering--.f64 61.5%

      \[\leadsto \mathsf{\_.f64}\left(1, \color{blue}{y}\right) \]

5. Simplified 61.5%

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

Alternative 6: 38.1% 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 81.2%

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

3. Taylor expanded in y around 0

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

5. Simplified 37.6%

   \[\leadsto \color{blue}{1} \]
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 2024193 
(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))))