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

Percentage Accurate: 77.6% → 100.0%

Time: 4.0s

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: 77.6% 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, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.2%

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

2. Taylor expanded in x around -inf 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-41}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+179}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.05e-41)
   (* y x)
   (if (<= y 1.0) 1.0 (if (<= y 8e+179) (- y) (* y x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.05e-41) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = 1.0;
	} else if (y <= 8e+179) {
		tmp = -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 (y <= (-2.05d-41)) then
        tmp = y * x
    else if (y <= 1.0d0) then
        tmp = 1.0d0
    else if (y <= 8d+179) then
        tmp = -y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.05e-41) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = 1.0;
	} else if (y <= 8e+179) {
		tmp = -y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.05e-41:
		tmp = y * x
	elif y <= 1.0:
		tmp = 1.0
	elif y <= 8e+179:
		tmp = -y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.05e-41)
		tmp = Float64(y * x);
	elseif (y <= 1.0)
		tmp = 1.0;
	elseif (y <= 8e+179)
		tmp = Float64(-y);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.05e-41)
		tmp = y * x;
	elseif (y <= 1.0)
		tmp = 1.0;
	elseif (y <= 8e+179)
		tmp = -y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.05e-41], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.0], 1.0, If[LessEqual[y, 8e+179], (-y), N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05000000000000007e-41 or 7.99999999999999984e179 < y

   1. Initial program 94.7%

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

   2. Taylor expanded in x around inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. unsub-neg 59.4%

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

      3. sub-neg 59.4%

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

      4. associate--r+ 64.6%

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

      5. metadata-eval 64.6%

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

      6. neg-sub0 64.6%

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

      7. remove-double-neg 64.6%

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

   4. Simplified 64.6%

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

   if -2.05000000000000007e-41 < y < 1

   1. Initial program 60.0%

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

   2. Taylor expanded in y around 0 81.8%

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

   if 1 < y < 7.99999999999999984e179

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 97.0%

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

      1. mul-1-neg 97.0%

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

      2. distribute-rgt-neg-in 97.0%

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

      3. sub-neg 97.0%

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

      4. distribute-neg-in 97.0%

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

      5. metadata-eval 97.0%

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

      6. remove-double-neg 97.0%

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

   4. Simplified 97.0%

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

   5. Taylor expanded in x around 0 73.5%

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

      1. neg-mul-1 73.5%

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

   7. Simplified 73.5%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-41}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+179}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-42} \lor \neg \left(y \leq 1.62 \cdot 10^{-68}\right):\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.4e-42) (not (<= y 1.62e-68))) (* y (+ x -1.0)) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.4e-42) || !(y <= 1.62e-68)) {
		tmp = y * (x + -1.0);
	} else {
		tmp = 1.0 - 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 <= (-4.4d-42)) .or. (.not. (y <= 1.62d-68))) then
        tmp = y * (x + (-1.0d0))
    else
        tmp = 1.0d0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.4e-42) || !(y <= 1.62e-68)) {
		tmp = y * (x + -1.0);
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.4e-42) or not (y <= 1.62e-68):
		tmp = y * (x + -1.0)
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.4e-42) || !(y <= 1.62e-68))
		tmp = Float64(y * Float64(x + -1.0));
	else
		tmp = Float64(1.0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.4e-42) || ~((y <= 1.62e-68)))
		tmp = y * (x + -1.0);
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.4e-42], N[Not[LessEqual[y, 1.62e-68]], $MachinePrecision]], N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4000000000000001e-42 or 1.62000000000000005e-68 < y

   1. Initial program 92.7%

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

   2. Taylor expanded in y around inf 93.9%

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

      1. mul-1-neg 93.9%

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

      2. distribute-rgt-neg-in 93.9%

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

      3. sub-neg 93.9%

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

      4. distribute-neg-in 93.9%

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

      5. metadata-eval 93.9%

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

      6. remove-double-neg 93.9%

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

   4. Simplified 93.9%

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

   if -4.4000000000000001e-42 < y < 1.62000000000000005e-68

   1. Initial program 60.5%

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

   2. Taylor expanded in x around 0 84.9%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-42} \lor \neg \left(y \leq 1.62 \cdot 10^{-68}\right):\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 4: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-40}:\\ \;\;\;\;y \cdot x - y\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-69}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.25e-40)
   (- (* y x) y)
   (if (<= y 7.5e-69) (- 1.0 y) (* y (+ x -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.25e-40) {
		tmp = (y * x) - y;
	} else if (y <= 7.5e-69) {
		tmp = 1.0 - y;
	} else {
		tmp = y * (x + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.25d-40)) then
        tmp = (y * x) - y
    else if (y <= 7.5d-69) then
        tmp = 1.0d0 - y
    else
        tmp = y * (x + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.25e-40) {
		tmp = (y * x) - y;
	} else if (y <= 7.5e-69) {
		tmp = 1.0 - y;
	} else {
		tmp = y * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.25e-40:
		tmp = (y * x) - y
	elif y <= 7.5e-69:
		tmp = 1.0 - y
	else:
		tmp = y * (x + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.25e-40)
		tmp = Float64(Float64(y * x) - y);
	elseif (y <= 7.5e-69)
		tmp = Float64(1.0 - y);
	else
		tmp = Float64(y * Float64(x + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.25e-40)
		tmp = (y * x) - y;
	elseif (y <= 7.5e-69)
		tmp = 1.0 - y;
	else
		tmp = y * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.25e-40], N[(N[(y * x), $MachinePrecision] - y), $MachinePrecision], If[LessEqual[y, 7.5e-69], N[(1.0 - y), $MachinePrecision], N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.24999999999999991e-40

   1. Initial program 91.6%

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

   2. Taylor expanded in y around inf 94.8%

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

      1. mul-1-neg 94.8%

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

      2. distribute-rgt-neg-in 94.8%

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

      3. sub-neg 94.8%

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

      4. distribute-neg-in 94.8%

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

      5. metadata-eval 94.8%

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

      6. remove-double-neg 94.8%

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

   4. Simplified 94.8%

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

      1. +-commutative 94.8%

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

      2. distribute-lft-in 94.8%

         \[\leadsto \color{blue}{y \cdot x + y \cdot -1} \]

      3. *-commutative 94.8%

         \[\leadsto y \cdot x + \color{blue}{-1 \cdot y} \]

      4. mul-1-neg 94.8%

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

   6. Applied egg-rr 94.8%

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

   7. Taylor expanded in y around 0 94.8%

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

      1. distribute-lft-out-- 94.8%

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

      2. *-rgt-identity 94.8%

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

   9. Simplified 94.8%

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

   if -1.24999999999999991e-40 < y < 7.5e-69

   1. Initial program 60.5%

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

   2. Taylor expanded in x around 0 84.9%

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

   if 7.5e-69 < y

   1. Initial program 93.7%

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

   2. Taylor expanded in y around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. distribute-rgt-neg-in 93.0%

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

      3. sub-neg 93.0%

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

      4. distribute-neg-in 93.0%

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

      5. metadata-eval 93.0%

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

      6. remove-double-neg 93.0%

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

   4. Simplified 93.0%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-40}:\\ \;\;\;\;y \cdot x - y\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-69}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 5: 87.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+45}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+22}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9e+45) (* y x) (if (<= x 4.8e+22) (- 1.0 y) (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9e+45) {
		tmp = y * x;
	} else if (x <= 4.8e+22) {
		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 <= (-9d+45)) then
        tmp = y * x
    else if (x <= 4.8d+22) 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 <= -9e+45) {
		tmp = y * x;
	} else if (x <= 4.8e+22) {
		tmp = 1.0 - y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9e+45:
		tmp = y * x
	elif x <= 4.8e+22:
		tmp = 1.0 - y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9e+45)
		tmp = Float64(y * x);
	elseif (x <= 4.8e+22)
		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 <= -9e+45)
		tmp = y * x;
	elseif (x <= 4.8e+22)
		tmp = 1.0 - y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9e+45], N[(y * x), $MachinePrecision], If[LessEqual[x, 4.8e+22], N[(1.0 - y), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.9999999999999997e45 or 4.8e22 < x

   1. Initial program 55.6%

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

   2. Taylor expanded in x around inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. unsub-neg 55.7%

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

      3. sub-neg 55.7%

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

      4. associate--r+ 77.4%

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

      5. metadata-eval 77.4%

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

      6. neg-sub0 77.4%

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

      7. remove-double-neg 77.4%

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

   4. Simplified 77.4%

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

   if -8.9999999999999997e45 < x < 4.8e22

   1. Initial program 95.1%

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

   2. Taylor expanded in x around 0 95.5%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+45}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+22}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 6: 61.6% 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 98.8%

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

      1. mul-1-neg 98.8%

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

      2. distribute-rgt-neg-in 98.8%

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

      3. sub-neg 98.8%

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

      4. distribute-neg-in 98.8%

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

      5. metadata-eval 98.8%

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

      6. remove-double-neg 98.8%

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

   4. Simplified 98.8%

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

   5. Taylor expanded in x around 0 43.3%

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

      1. neg-mul-1 43.3%

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

   7. Simplified 43.3%

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

   if -1 < y < 1

   1. Initial program 58.9%

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

   2. Taylor expanded in y around 0 77.4%

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

4. Final simplification 62.2%

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

Alternative 7: 37.9% 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 77.2%

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

2. Taylor expanded in y around 0 44.1%

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

3. Final simplification 44.1%

   \[\leadsto 1 \]

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 2023238 
(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))))