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

Percentage Accurate: 100.0% → 100.0%

Time: 7.1s

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

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

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]

Derivation

1. Initial program 100.0%

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

Alternative 2: 86.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5400000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-45}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 230:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5400000.0)
   (- 1.0 (/ x y))
   (if (<= y -9e-45)
     (/ y (+ y -1.0))
     (if (<= y 230.0) (/ x (- 1.0 y)) (+ 1.0 (/ (- 1.0 x) y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5400000.0) {
		tmp = 1.0 - (x / y);
	} else if (y <= -9e-45) {
		tmp = y / (y + -1.0);
	} else if (y <= 230.0) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0 + ((1.0 - 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 <= (-5400000.0d0)) then
        tmp = 1.0d0 - (x / y)
    else if (y <= (-9d-45)) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 230.0d0) then
        tmp = x / (1.0d0 - y)
    else
        tmp = 1.0d0 + ((1.0d0 - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5400000.0) {
		tmp = 1.0 - (x / y);
	} else if (y <= -9e-45) {
		tmp = y / (y + -1.0);
	} else if (y <= 230.0) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0 + ((1.0 - x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5400000.0:
		tmp = 1.0 - (x / y)
	elif y <= -9e-45:
		tmp = y / (y + -1.0)
	elif y <= 230.0:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0 + ((1.0 - x) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5400000.0)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (y <= -9e-45)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 230.0)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5400000.0)
		tmp = 1.0 - (x / y);
	elseif (y <= -9e-45)
		tmp = y / (y + -1.0);
	elseif (y <= 230.0)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0 + ((1.0 - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5400000.0], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9e-45], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 230.0], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.4e6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.9%

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

   4. Taylor expanded in y around inf 98.6%

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

      1. neg-mul-1 98.6%

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

   6. Simplified 98.6%

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

   7. Taylor expanded in x around 0 98.6%

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

      1. neg-mul-1 98.6%

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

      2. unsub-neg 98.6%

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

   9. Simplified 98.6%

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

   if -5.4e6 < y < -8.9999999999999997e-45

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 67.0%

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

      1. neg-mul-1 67.0%

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

      2. distribute-neg-frac2 67.0%

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

      3. neg-sub0 67.0%

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

      4. associate--r- 67.0%

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

      5. metadata-eval 67.0%

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

   5. Simplified 67.0%

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

   if -8.9999999999999997e-45 < y < 230

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.5%

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

   if 230 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.4%

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

      1. +-commutative 99.4%

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

      2. mul-1-neg 99.4%

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

      3. sub-neg 99.4%

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

      4. div-sub 99.4%

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

   5. Simplified 99.4%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5400000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-45}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 230:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -1500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 19000:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -1500000.0)
     t_0
     (if (<= y -2.1e-46)
       (/ y (+ y -1.0))
       (if (<= y 19000.0) (/ x (- 1.0 y)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -1500000.0) {
		tmp = t_0;
	} else if (y <= -2.1e-46) {
		tmp = y / (y + -1.0);
	} else if (y <= 19000.0) {
		tmp = x / (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 = 1.0d0 - (x / y)
    if (y <= (-1500000.0d0)) then
        tmp = t_0
    else if (y <= (-2.1d-46)) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 19000.0d0) then
        tmp = x / (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 = 1.0 - (x / y);
	double tmp;
	if (y <= -1500000.0) {
		tmp = t_0;
	} else if (y <= -2.1e-46) {
		tmp = y / (y + -1.0);
	} else if (y <= 19000.0) {
		tmp = x / (1.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -1500000.0:
		tmp = t_0
	elif y <= -2.1e-46:
		tmp = y / (y + -1.0)
	elif y <= 19000.0:
		tmp = x / (1.0 - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -1500000.0)
		tmp = t_0;
	elseif (y <= -2.1e-46)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 19000.0)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -1500000.0)
		tmp = t_0;
	elseif (y <= -2.1e-46)
		tmp = y / (y + -1.0);
	elseif (y <= 19000.0)
		tmp = x / (1.0 - y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1500000.0], t$95$0, If[LessEqual[y, -2.1e-46], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 19000.0], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5e6 or 19000 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around inf 98.4%

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

      1. neg-mul-1 98.4%

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

   6. Simplified 98.4%

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

   7. Taylor expanded in x around 0 98.5%

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

      1. neg-mul-1 98.5%

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

      2. unsub-neg 98.5%

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

   9. Simplified 98.5%

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

   if -1.5e6 < y < -2.09999999999999987e-46

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 67.0%

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

      1. neg-mul-1 67.0%

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

      2. distribute-neg-frac2 67.0%

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

      3. neg-sub0 67.0%

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

      4. associate--r- 67.0%

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

      5. metadata-eval 67.0%

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

   5. Simplified 67.0%

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

   if -2.09999999999999987e-46 < y < 19000

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.5%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1500000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-46}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 19000:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{+86}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -0.75:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.18e+86)
   1.0
   (if (<= y -0.75) (/ x (- y)) (if (<= y 1.0) (+ x (* x y)) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.18e+86) {
		tmp = 1.0;
	} else if (y <= -0.75) {
		tmp = x / -y;
	} else if (y <= 1.0) {
		tmp = x + (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 <= (-1.18d+86)) then
        tmp = 1.0d0
    else if (y <= (-0.75d0)) then
        tmp = x / -y
    else if (y <= 1.0d0) then
        tmp = x + (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 <= -1.18e+86) {
		tmp = 1.0;
	} else if (y <= -0.75) {
		tmp = x / -y;
	} else if (y <= 1.0) {
		tmp = x + (x * y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.18e+86:
		tmp = 1.0
	elif y <= -0.75:
		tmp = x / -y
	elif y <= 1.0:
		tmp = x + (x * y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.18e+86)
		tmp = 1.0;
	elseif (y <= -0.75)
		tmp = Float64(x / Float64(-y));
	elseif (y <= 1.0)
		tmp = Float64(x + Float64(x * y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.18e+86)
		tmp = 1.0;
	elseif (y <= -0.75)
		tmp = x / -y;
	elseif (y <= 1.0)
		tmp = x + (x * y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.18e+86], 1.0, If[LessEqual[y, -0.75], N[(x / (-y)), $MachinePrecision], If[LessEqual[y, 1.0], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.18e86 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 78.9%

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

   if -1.18e86 < y < -0.75

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.3%

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

   4. Taylor expanded in y around inf 59.1%

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

      1. associate-*r/ 59.1%

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

      2. neg-mul-1 59.1%

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

   6. Simplified 59.1%

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

   if -0.75 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.7%

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

   4. Taylor expanded in y around 0 71.0%

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

      1. *-commutative 71.0%

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

   6. Simplified 71.0%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{+86}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -0.75:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+83}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.9e+83) 1.0 (if (<= y -1.0) (/ x (- y)) (if (<= y 1.0) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.9e+83) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = x / -y;
	} 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 <= (-1.9d+83)) then
        tmp = 1.0d0
    else if (y <= (-1.0d0)) then
        tmp = x / -y
    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 <= -1.9e+83) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = x / -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.9e+83:
		tmp = 1.0
	elif y <= -1.0:
		tmp = x / -y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.9e+83)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = Float64(x / Float64(-y));
	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 <= -1.9e+83)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = x / -y;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.9e+83], 1.0, If[LessEqual[y, -1.0], N[(x / (-y)), $MachinePrecision], If[LessEqual[y, 1.0], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9000000000000001e83 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 78.9%

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

   if -1.9000000000000001e83 < y < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.3%

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

   4. Taylor expanded in y around inf 59.1%

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

      1. associate-*r/ 59.1%

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

      2. neg-mul-1 59.1%

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

   6. Simplified 59.1%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 70.7%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+83}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -920 \lor \neg \left(y \leq 110\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -920.0) (not (<= y 110.0))) (- 1.0 (/ x y)) (/ x (- 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -920.0) || !(y <= 110.0)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (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 <= (-920.0d0)) .or. (.not. (y <= 110.0d0))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x / (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -920.0) || !(y <= 110.0)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -920.0) or not (y <= 110.0):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (1.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -920.0) || !(y <= 110.0))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x / Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -920.0) || ~((y <= 110.0)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -920.0], N[Not[LessEqual[y, 110.0]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -920 or 110 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around inf 97.3%

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

      1. neg-mul-1 97.3%

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

   6. Simplified 97.3%

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

   7. Taylor expanded in x around 0 97.3%

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

      1. neg-mul-1 97.3%

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

      2. unsub-neg 97.3%

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

   9. Simplified 97.3%

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

   if -920 < y < 110

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.9%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -920 \lor \neg \left(y \leq 110\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0112 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -0.0112) (not (<= y 1.0))) (- 1.0 (/ x y)) (+ x (* x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -0.0112) || !(y <= 1.0)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x + (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 <= (-0.0112d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -0.0112) || !(y <= 1.0)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x + (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -0.0112) or not (y <= 1.0):
		tmp = 1.0 - (x / y)
	else:
		tmp = x + (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -0.0112) || !(y <= 1.0))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -0.0112) || ~((y <= 1.0)))
		tmp = 1.0 - (x / y);
	else
		tmp = x + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -0.0112], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0111999999999999999 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around inf 96.7%

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

      1. neg-mul-1 96.7%

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

   6. Simplified 96.7%

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

   7. Taylor expanded in x around 0 96.7%

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

      1. neg-mul-1 96.7%

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

      2. unsub-neg 96.7%

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

   9. Simplified 96.7%

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

   if -0.0111999999999999999 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.7%

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

   4. Taylor expanded in y around 0 71.0%

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

      1. *-commutative 71.0%

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

   6. Simplified 71.0%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0112 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -160:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -160.0) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -160.0) {
		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 <= (-160.0d0)) 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 <= -160.0) {
		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 <= -160.0:
		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 <= -160.0)
		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 <= -160.0)
		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, -160.0], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -160 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 71.0%

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

   if -160 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 70.3%

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

Alternative 9: 38.1% 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 33.5%

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

Reproduce

herbie shell --seed 2024132 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))