Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, C

Percentage Accurate: 100.0% → 100.0%

Time: 4.9s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

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]

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{1 - y} \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto \frac{y - x}{y + -1} \]
4. Add Preprocessing

Alternative 2: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-6}:\\ \;\;\;\;x - y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -9.5e-6)
   (/ y (+ y -1.0))
   (if (<= y 1.55e-6) (- x y) (if (<= y 2.1e+77) (/ x (- 1.0 y)) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -9.5e-6) {
		tmp = y / (y + -1.0);
	} else if (y <= 1.55e-6) {
		tmp = x - y;
	} else if (y <= 2.1e+77) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 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 <= (-9.5d-6)) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 1.55d-6) then
        tmp = x - y
    else if (y <= 2.1d+77) then
        tmp = x / (1.0d0 - y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -9.5e-6) {
		tmp = y / (y + -1.0);
	} else if (y <= 1.55e-6) {
		tmp = x - y;
	} else if (y <= 2.1e+77) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -9.5e-6:
		tmp = y / (y + -1.0)
	elif y <= 1.55e-6:
		tmp = x - y
	elif y <= 2.1e+77:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -9.5e-6)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 1.55e-6)
		tmp = Float64(x - y);
	elseif (y <= 2.1e+77)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -9.5e-6)
		tmp = y / (y + -1.0);
	elseif (y <= 1.55e-6)
		tmp = x - y;
	elseif (y <= 2.1e+77)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -9.5e-6], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-6], N[(x - y), $MachinePrecision], If[LessEqual[y, 2.1e+77], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.5000000000000005e-6

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 75.1%

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

      1. neg-mul-1 75.1%

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

      2. distribute-neg-frac2 75.1%

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

      3. neg-sub0 75.1%

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

      4. associate--r- 75.1%

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

      5. metadata-eval 75.1%

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

   5. Simplified 75.1%

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

   if -9.5000000000000005e-6 < y < 1.55e-6

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

      3. mul-1-neg 99.6%

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

      4. sub-neg 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around 0 99.0%

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

   if 1.55e-6 < y < 2.0999999999999999e77

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.7%

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

   if 2.0999999999999999e77 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 82.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-6}:\\ \;\;\;\;x - y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -15:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.000116:\\ \;\;\;\;x - y\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -15.0)
   1.0
   (if (<= y 0.000116) (- x y) (if (<= y 8.2e+76) (/ x (- 1.0 y)) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -15.0) {
		tmp = 1.0;
	} else if (y <= 0.000116) {
		tmp = x - y;
	} else if (y <= 8.2e+76) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 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 <= (-15.0d0)) then
        tmp = 1.0d0
    else if (y <= 0.000116d0) then
        tmp = x - y
    else if (y <= 8.2d+76) then
        tmp = x / (1.0d0 - y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -15.0) {
		tmp = 1.0;
	} else if (y <= 0.000116) {
		tmp = x - y;
	} else if (y <= 8.2e+76) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -15.0:
		tmp = 1.0
	elif y <= 0.000116:
		tmp = x - y
	elif y <= 8.2e+76:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -15.0)
		tmp = 1.0;
	elseif (y <= 0.000116)
		tmp = Float64(x - y);
	elseif (y <= 8.2e+76)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -15.0)
		tmp = 1.0;
	elseif (y <= 0.000116)
		tmp = x - y;
	elseif (y <= 8.2e+76)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -15.0], 1.0, If[LessEqual[y, 0.000116], N[(x - y), $MachinePrecision], If[LessEqual[y, 8.2e+76], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -15 or 8.1999999999999997e76 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.0%

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

   if -15 < y < 1.16e-4

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

      3. mul-1-neg 99.6%

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

      4. sub-neg 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around 0 99.0%

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

   if 1.16e-4 < y < 8.1999999999999997e76

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.7%

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

Alternative 4: 85.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -86:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+77}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -86.0)
   1.0
   (if (<= y 1.0) (- x y) (if (<= y 1.25e+77) (/ (- x) y) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -86.0) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x - y;
	} else if (y <= 1.25e+77) {
		tmp = -x / y;
	} else {
		tmp = 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 <= (-86.0d0)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x - y
    else if (y <= 1.25d+77) then
        tmp = -x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -86.0) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x - y;
	} else if (y <= 1.25e+77) {
		tmp = -x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -86.0:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x - y
	elif y <= 1.25e+77:
		tmp = -x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -86.0)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = Float64(x - y);
	elseif (y <= 1.25e+77)
		tmp = Float64(Float64(-x) / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -86.0)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x - y;
	elseif (y <= 1.25e+77)
		tmp = -x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -86.0], 1.0, If[LessEqual[y, 1.0], N[(x - y), $MachinePrecision], If[LessEqual[y, 1.25e+77], N[((-x) / y), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -86 or 1.25000000000000001e77 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.0%

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

   if -86 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. unsub-neg 98.5%

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

      3. mul-1-neg 98.5%

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

      4. sub-neg 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in x around 0 97.9%

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

   if 1 < y < 1.25000000000000001e77

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 82.3%

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

   4. Taylor expanded in y around inf 72.4%

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

      1. neg-mul-1 72.4%

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

      2. distribute-neg-frac 72.4%

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

   6. Simplified 72.4%

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

Alternative 5: 98.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0)))
   (- 1.0 (/ (+ x -1.0) y))
   (+ x (* y (+ x -1.0)))))

C

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

Java

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

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.0):
		tmp = 1.0 - ((x + -1.0) / y)
	else:
		tmp = x + (y * (x + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(1.0 - Float64(Float64(x + -1.0) / y));
	else
		tmp = Float64(x + Float64(y * Float64(x + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.0)))
		tmp = 1.0 - ((x + -1.0) / y);
	else
		tmp = x + (y * (x + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(1.0 - N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.5%

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

      1. +-commutative 98.5%

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

      2. mul-1-neg 98.5%

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

      3. sub-neg 98.5%

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

      4. div-sub 98.5%

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

   5. Simplified 98.5%

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

   if -1 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. unsub-neg 98.5%

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

      3. mul-1-neg 98.5%

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

      4. sub-neg 98.5%

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

   5. Simplified 98.5%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;x - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.25) (not (<= y 1.0))) (- 1.0 (/ (+ x -1.0) y)) (- x y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.25) || !(y <= 1.0)) {
		tmp = 1.0 - ((x + -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 ((y <= (-1.25d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = 1.0d0 - ((x + (-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 ((y <= -1.25) || !(y <= 1.0)) {
		tmp = 1.0 - ((x + -1.0) / y);
	} else {
		tmp = x - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.25) or not (y <= 1.0):
		tmp = 1.0 - ((x + -1.0) / y)
	else:
		tmp = x - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.25) || !(y <= 1.0))
		tmp = Float64(1.0 - Float64(Float64(x + -1.0) / y));
	else
		tmp = Float64(x - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.25) || ~((y <= 1.0)))
		tmp = 1.0 - ((x + -1.0) / y);
	else
		tmp = x - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.25], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(1.0 - N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.5%

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

      1. +-commutative 98.5%

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

      2. mul-1-neg 98.5%

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

      3. sub-neg 98.5%

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

      4. div-sub 98.5%

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

   5. Simplified 98.5%

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

   if -1.25 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. unsub-neg 98.5%

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

      3. mul-1-neg 98.5%

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

      4. sub-neg 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in x around 0 97.9%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;x - y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -55:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -55.0) 1.0 (if (<= y 1.0) (- x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -55.0) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x - y;
	} else {
		tmp = 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 <= (-55.0d0)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x - y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -55.0) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x - y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -55.0:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x - y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -55.0)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = Float64(x - y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -55.0)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x - y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -55.0], 1.0, If[LessEqual[y, 1.0], N[(x - y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -55 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.1%

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

   if -55 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. unsub-neg 98.5%

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

      3. mul-1-neg 98.5%

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

      4. sub-neg 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in x around 0 97.9%

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

Alternative 8: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.145:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -0.145) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.145) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 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 <= (-0.145d0)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -0.145) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.145:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.145)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.145)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.145], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -0.14499999999999999 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.1%

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

   if -0.14499999999999999 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 75.9%

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

Alternative 9: 39.3% accurate, 7.0× 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 100.0%

   \[\frac{x - y}{1 - y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf 37.5%

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

Reproduce

herbie shell --seed 2024103 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))