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

Percentage Accurate: 100.0% → 100.0%

Time: 5.2s

Alternatives: 6

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. Final simplification 100.0%

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

Alternative 2: 72.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+59}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+26}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -3:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.7e+59)
   1.0
   (if (<= y -4e+26)
     (/ (- x) y)
     (if (<= y -3.0)
       1.0
       (if (<= y -3.8e-63)
         (* y (- -1.0 y))
         (if (<= y 1.0) (* x (+ y 1.0)) 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.7e+59) {
		tmp = 1.0;
	} else if (y <= -4e+26) {
		tmp = -x / y;
	} else if (y <= -3.0) {
		tmp = 1.0;
	} else if (y <= -3.8e-63) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.0) {
		tmp = x * (y + 1.0);
	} 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 <= (-1.7d+59)) then
        tmp = 1.0d0
    else if (y <= (-4d+26)) then
        tmp = -x / y
    else if (y <= (-3.0d0)) then
        tmp = 1.0d0
    else if (y <= (-3.8d-63)) then
        tmp = y * ((-1.0d0) - y)
    else if (y <= 1.0d0) then
        tmp = x * (y + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.7e+59) {
		tmp = 1.0;
	} else if (y <= -4e+26) {
		tmp = -x / y;
	} else if (y <= -3.0) {
		tmp = 1.0;
	} else if (y <= -3.8e-63) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.0) {
		tmp = x * (y + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.7e+59:
		tmp = 1.0
	elif y <= -4e+26:
		tmp = -x / y
	elif y <= -3.0:
		tmp = 1.0
	elif y <= -3.8e-63:
		tmp = y * (-1.0 - y)
	elif y <= 1.0:
		tmp = x * (y + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.7e+59)
		tmp = 1.0;
	elseif (y <= -4e+26)
		tmp = Float64(Float64(-x) / y);
	elseif (y <= -3.0)
		tmp = 1.0;
	elseif (y <= -3.8e-63)
		tmp = Float64(y * Float64(-1.0 - y));
	elseif (y <= 1.0)
		tmp = Float64(x * Float64(y + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.7e+59)
		tmp = 1.0;
	elseif (y <= -4e+26)
		tmp = -x / y;
	elseif (y <= -3.0)
		tmp = 1.0;
	elseif (y <= -3.8e-63)
		tmp = y * (-1.0 - y);
	elseif (y <= 1.0)
		tmp = x * (y + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.7e+59], 1.0, If[LessEqual[y, -4e+26], N[((-x) / y), $MachinePrecision], If[LessEqual[y, -3.0], 1.0, If[LessEqual[y, -3.8e-63], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.70000000000000003e59 or -4.00000000000000019e26 < y < -3 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 78.6%

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

   if -1.70000000000000003e59 < y < -4.00000000000000019e26

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.5%

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

   4. Taylor expanded in y around inf 78.5%

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

      1. associate-*r/ 78.5%

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

      2. neg-mul-1 78.5%

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

   6. Simplified 78.5%

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

   if -3 < y < -3.80000000000000017e-63

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 59.3%

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

      1. neg-mul-1 59.3%

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

      2. distribute-neg-frac2 59.3%

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

      3. neg-sub0 59.3%

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

      4. associate--r- 59.3%

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

      5. metadata-eval 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in y around 0 59.6%

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

      1. sub-neg 59.6%

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

      2. metadata-eval 59.6%

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

      3. neg-mul-1 59.6%

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

      4. +-commutative 59.6%

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

      5. sub-neg 59.6%

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

   8. Simplified 59.6%

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

   if -3.80000000000000017e-63 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.1%

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

   4. Taylor expanded in y around 0 71.1%

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

      1. *-commutative 71.1%

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

      2. distribute-rgt1-in 71.1%

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

   6. Applied egg-rr 71.1%

      \[\leadsto \color{blue}{\left(y + 1\right) \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+59}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+26}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -3:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+58}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-63} \lor \neg \left(y \leq 5 \cdot 10^{-79}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.8e+58)
   1.0
   (if (<= y -3.4e+27)
     (/ (- x) y)
     (if (or (<= y -3.9e-63) (not (<= y 5e-79)))
       (/ y (+ y -1.0))
       (/ x (- 1.0 y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.8e+58) {
		tmp = 1.0;
	} else if (y <= -3.4e+27) {
		tmp = -x / y;
	} else if ((y <= -3.9e-63) || !(y <= 5e-79)) {
		tmp = y / (y + -1.0);
	} 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 <= (-4.8d+58)) then
        tmp = 1.0d0
    else if (y <= (-3.4d+27)) then
        tmp = -x / y
    else if ((y <= (-3.9d-63)) .or. (.not. (y <= 5d-79))) then
        tmp = y / (y + (-1.0d0))
    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 <= -4.8e+58) {
		tmp = 1.0;
	} else if (y <= -3.4e+27) {
		tmp = -x / y;
	} else if ((y <= -3.9e-63) || !(y <= 5e-79)) {
		tmp = y / (y + -1.0);
	} else {
		tmp = x / (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.8e+58:
		tmp = 1.0
	elif y <= -3.4e+27:
		tmp = -x / y
	elif (y <= -3.9e-63) or not (y <= 5e-79):
		tmp = y / (y + -1.0)
	else:
		tmp = x / (1.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.8e+58)
		tmp = 1.0;
	elseif (y <= -3.4e+27)
		tmp = Float64(Float64(-x) / y);
	elseif ((y <= -3.9e-63) || !(y <= 5e-79))
		tmp = Float64(y / Float64(y + -1.0));
	else
		tmp = Float64(x / Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.8e+58)
		tmp = 1.0;
	elseif (y <= -3.4e+27)
		tmp = -x / y;
	elseif ((y <= -3.9e-63) || ~((y <= 5e-79)))
		tmp = y / (y + -1.0);
	else
		tmp = x / (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.8e+58], 1.0, If[LessEqual[y, -3.4e+27], N[((-x) / y), $MachinePrecision], If[Or[LessEqual[y, -3.9e-63], N[Not[LessEqual[y, 5e-79]], $MachinePrecision]], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.8e58

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.6%

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

   if -4.8e58 < y < -3.4e27

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.5%

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

   4. Taylor expanded in y around inf 78.5%

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

      1. associate-*r/ 78.5%

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

      2. neg-mul-1 78.5%

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

   6. Simplified 78.5%

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

   if -3.4e27 < y < -3.90000000000000022e-63 or 4.99999999999999999e-79 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.4%

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

      1. neg-mul-1 73.4%

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

      2. distribute-neg-frac2 73.4%

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

      3. neg-sub0 73.4%

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

      4. associate--r- 73.4%

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

      5. metadata-eval 73.4%

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

   5. Simplified 73.4%

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

   if -3.90000000000000022e-63 < y < 4.99999999999999999e-79

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+58}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-63} \lor \neg \left(y \leq 5 \cdot 10^{-79}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+58}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -14.5:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.45e+58)
   1.0
   (if (<= y -7.5e+26)
     (/ (- x) y)
     (if (<= y -14.5) 1.0 (if (<= y 1.0) x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.45e+58) {
		tmp = 1.0;
	} else if (y <= -7.5e+26) {
		tmp = -x / y;
	} else if (y <= -14.5) {
		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 <= (-1.45d+58)) then
        tmp = 1.0d0
    else if (y <= (-7.5d+26)) then
        tmp = -x / y
    else if (y <= (-14.5d0)) 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 <= -1.45e+58) {
		tmp = 1.0;
	} else if (y <= -7.5e+26) {
		tmp = -x / y;
	} else if (y <= -14.5) {
		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 <= -1.45e+58:
		tmp = 1.0
	elif y <= -7.5e+26:
		tmp = -x / y
	elif y <= -14.5:
		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 <= -1.45e+58)
		tmp = 1.0;
	elseif (y <= -7.5e+26)
		tmp = Float64(Float64(-x) / y);
	elseif (y <= -14.5)
		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 <= -1.45e+58)
		tmp = 1.0;
	elseif (y <= -7.5e+26)
		tmp = -x / y;
	elseif (y <= -14.5)
		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, -1.45e+58], 1.0, If[LessEqual[y, -7.5e+26], N[((-x) / y), $MachinePrecision], If[LessEqual[y, -14.5], 1.0, If[LessEqual[y, 1.0], x, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45000000000000001e58 or -7.49999999999999941e26 < y < -14.5 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 78.6%

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

   if -1.45000000000000001e58 < y < -7.49999999999999941e26

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.5%

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

   4. Taylor expanded in y around inf 78.5%

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

      1. associate-*r/ 78.5%

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

      2. neg-mul-1 78.5%

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

   6. Simplified 78.5%

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

   if -14.5 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.2%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+58}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -14.5:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -18:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -18.0) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -18.0) {
		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 <= (-18.0d0)) 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 <= -18.0) {
		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 <= -18.0:
		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 <= -18.0)
		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 <= -18.0)
		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, -18.0], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -18 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 75.1%

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

   if -18 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.2%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -18:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.8% 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 41.9%

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

4. Final simplification 41.9%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024050 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))