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

Percentage Accurate: 100.0% → 100.0%

Time: 5.9s

Alternatives: 9

Speedup: 1.0×

• could not determine a ground truth

  1. x = 2.4632067629871276e-105
  2. y = -1.900946917666477e-106

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. Final simplification 100.0%

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

Alternative 2: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - y}\\ \mathbf{if}\;x \leq -24000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-66} \lor \neg \left(x \leq 2 \cdot 10^{+41}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 y))))
   (if (<= x -24000000000.0)
     t_0
     (if (<= x -2e-39)
       1.0
       (if (or (<= x -1.95e-66) (not (<= x 2e+41))) t_0 (/ y (+ y -1.0)))))))

C

double code(double x, double y) {
	double t_0 = x / (1.0 - y);
	double tmp;
	if (x <= -24000000000.0) {
		tmp = t_0;
	} else if (x <= -2e-39) {
		tmp = 1.0;
	} else if ((x <= -1.95e-66) || !(x <= 2e+41)) {
		tmp = t_0;
	} else {
		tmp = y / (y + -1.0);
	}
	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 = x / (1.0d0 - y)
    if (x <= (-24000000000.0d0)) then
        tmp = t_0
    else if (x <= (-2d-39)) then
        tmp = 1.0d0
    else if ((x <= (-1.95d-66)) .or. (.not. (x <= 2d+41))) then
        tmp = t_0
    else
        tmp = y / (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (1.0 - y);
	double tmp;
	if (x <= -24000000000.0) {
		tmp = t_0;
	} else if (x <= -2e-39) {
		tmp = 1.0;
	} else if ((x <= -1.95e-66) || !(x <= 2e+41)) {
		tmp = t_0;
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (1.0 - y)
	tmp = 0
	if x <= -24000000000.0:
		tmp = t_0
	elif x <= -2e-39:
		tmp = 1.0
	elif (x <= -1.95e-66) or not (x <= 2e+41):
		tmp = t_0
	else:
		tmp = y / (y + -1.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(1.0 - y))
	tmp = 0.0
	if (x <= -24000000000.0)
		tmp = t_0;
	elseif (x <= -2e-39)
		tmp = 1.0;
	elseif ((x <= -1.95e-66) || !(x <= 2e+41))
		tmp = t_0;
	else
		tmp = Float64(y / Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (1.0 - y);
	tmp = 0.0;
	if (x <= -24000000000.0)
		tmp = t_0;
	elseif (x <= -2e-39)
		tmp = 1.0;
	elseif ((x <= -1.95e-66) || ~((x <= 2e+41)))
		tmp = t_0;
	else
		tmp = y / (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -24000000000.0], t$95$0, If[LessEqual[x, -2e-39], 1.0, If[Or[LessEqual[x, -1.95e-66], N[Not[LessEqual[x, 2e+41]], $MachinePrecision]], t$95$0, N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4e10 or -1.99999999999999986e-39 < x < -1.94999999999999991e-66 or 2.00000000000000001e41 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.2%

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

   if -2.4e10 < x < -1.99999999999999986e-39

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   if -1.94999999999999991e-66 < x < 2.00000000000000001e41

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.0%

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

      1. neg-mul-1 78.0%

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

      2. distribute-neg-frac2 78.0%

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

      3. neg-sub0 78.0%

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

      4. associate--r- 78.0%

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

      5. metadata-eval 78.0%

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

   5. Simplified 78.0%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -24000000000:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-39}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-66} \lor \neg \left(x \leq 2 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.6e-12)
   1.0
   (if (<= y 1.0) x (if (<= y 1.3e+55) (/ x (- y)) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.6e-12) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else if (y <= 1.3e+55) {
		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 <= (-4.6d-12)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x
    else if (y <= 1.3d+55) 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 <= -4.6e-12) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else if (y <= 1.3e+55) {
		tmp = x / -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.6e-12:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x
	elif y <= 1.3e+55:
		tmp = x / -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.6e-12)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	elseif (y <= 1.3e+55)
		tmp = Float64(x / Float64(-y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.6e-12)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	elseif (y <= 1.3e+55)
		tmp = x / -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.6e-12], 1.0, If[LessEqual[y, 1.0], x, If[LessEqual[y, 1.3e+55], N[(x / (-y)), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.59999999999999979e-12 or 1.3e55 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.5%

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

   if -4.59999999999999979e-12 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.1%

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

   if 1 < y < 1.3e55

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.5%

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

   4. Taylor expanded in y around inf 70.0%

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

      1. associate-*r/ 70.0%

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

      2. neg-mul-1 70.0%

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

   6. Simplified 70.0%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + x \cdot y\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.6e-12)
   1.0
   (if (<= y 1.0) (+ x (* x y)) (if (<= y 1.55e+55) (/ x (- y)) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.6e-12) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x + (x * y);
	} else if (y <= 1.55e+55) {
		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 <= (-4.6d-12)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x + (x * y)
    else if (y <= 1.55d+55) 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 <= -4.6e-12) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x + (x * y);
	} else if (y <= 1.55e+55) {
		tmp = x / -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.6e-12:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x + (x * y)
	elif y <= 1.55e+55:
		tmp = x / -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.6e-12)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = Float64(x + Float64(x * y));
	elseif (y <= 1.55e+55)
		tmp = Float64(x / Float64(-y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.6e-12)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x + (x * y);
	elseif (y <= 1.55e+55)
		tmp = x / -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.6e-12], 1.0, If[LessEqual[y, 1.0], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+55], N[(x / (-y)), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.59999999999999979e-12 or 1.54999999999999997e55 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.5%

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

   if -4.59999999999999979e-12 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.7%

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

   4. Taylor expanded in y around 0 76.7%

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

   if 1 < y < 1.54999999999999997e55

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.5%

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

   4. Taylor expanded in y around inf 70.0%

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

      1. associate-*r/ 70.0%

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

      2. neg-mul-1 70.0%

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

   6. Simplified 70.0%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + x \cdot y\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -41000 \lor \neg \left(y \leq 4.5 \cdot 10^{+14}\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -41000.0) (not (<= y 4.5e+14)))
   (+ 1.0 (/ (- 1.0 x) y))
   (/ x (- 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -41000.0) || !(y <= 4.5e+14)) {
		tmp = 1.0 + ((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 <= (-41000.0d0)) .or. (.not. (y <= 4.5d+14))) then
        tmp = 1.0d0 + ((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 <= -41000.0) || !(y <= 4.5e+14)) {
		tmp = 1.0 + ((1.0 - x) / y);
	} else {
		tmp = x / (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -41000.0) or not (y <= 4.5e+14):
		tmp = 1.0 + ((1.0 - x) / y)
	else:
		tmp = x / (1.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -41000.0) || !(y <= 4.5e+14))
		tmp = Float64(1.0 + Float64(Float64(1.0 - 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 <= -41000.0) || ~((y <= 4.5e+14)))
		tmp = 1.0 + ((1.0 - x) / y);
	else
		tmp = x / (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -41000.0], N[Not[LessEqual[y, 4.5e+14]], $MachinePrecision]], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -41000 or 4.5e14 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.8%

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

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. div-sub 99.8%

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

   5. Simplified 99.8%

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

   if -41000 < y < 4.5e14

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.5%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -41000 \lor \neg \left(y \leq 4.5 \cdot 10^{+14}\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.5% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0)))
   (+ 1.0 (/ (- 1.0 x) 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 + ((1.0 - x) / 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 + ((1.0d0 - x) / 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 + ((1.0 - x) / 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 + ((1.0 - x) / 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(1.0 - x) / 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 + ((1.0 - x) / 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[(1.0 - x), $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 98.0%

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

      1. +-commutative 98.0%

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

      2. mul-1-neg 98.0%

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

      3. sub-neg 98.0%

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

      4. div-sub 98.0%

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

   5. Simplified 98.0%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

      3. mul-1-neg 99.8%

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

      4. sub-neg 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 98.8%

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

Alternative 7: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+51}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6e+51) 1.0 (if (<= y 1.62e+55) (/ x (- 1.0 y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6e+51) {
		tmp = 1.0;
	} else if (y <= 1.62e+55) {
		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 <= (-6d+51)) then
        tmp = 1.0d0
    else if (y <= 1.62d+55) 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 <= -6e+51) {
		tmp = 1.0;
	} else if (y <= 1.62e+55) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6e+51:
		tmp = 1.0
	elif y <= 1.62e+55:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6e+51)
		tmp = 1.0;
	elseif (y <= 1.62e+55)
		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 <= -6e+51)
		tmp = 1.0;
	elseif (y <= 1.62e+55)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6e+51], 1.0, If[LessEqual[y, 1.62e+55], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -6e51 or 1.62000000000000013e55 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 76.8%

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

   if -6e51 < y < 1.62000000000000013e55

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.4%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+51}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.6e-12) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.6e-12) {
		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 <= (-4.6d-12)) 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 <= -4.6e-12) {
		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 <= -4.6e-12:
		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 <= -4.6e-12)
		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 <= -4.6e-12)
		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, -4.6e-12], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.59999999999999979e-12 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 68.8%

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

   if -4.59999999999999979e-12 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.1%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 39.2% 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 38.4%

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

4. Final simplification 38.4%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024079 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))