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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

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: 71.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3600000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\frac{y}{-1}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+83}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3600000.0)
   1.0
   (if (<= y 8e-110)
     x
     (if (<= y 1.0) (/ y -1.0) (if (<= y 2.9e+83) (/ (- x) y) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3600000.0) {
		tmp = 1.0;
	} else if (y <= 8e-110) {
		tmp = x;
	} else if (y <= 1.0) {
		tmp = y / -1.0;
	} else if (y <= 2.9e+83) {
		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 <= (-3600000.0d0)) then
        tmp = 1.0d0
    else if (y <= 8d-110) then
        tmp = x
    else if (y <= 1.0d0) then
        tmp = y / (-1.0d0)
    else if (y <= 2.9d+83) 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 <= -3600000.0) {
		tmp = 1.0;
	} else if (y <= 8e-110) {
		tmp = x;
	} else if (y <= 1.0) {
		tmp = y / -1.0;
	} else if (y <= 2.9e+83) {
		tmp = -x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3600000.0:
		tmp = 1.0
	elif y <= 8e-110:
		tmp = x
	elif y <= 1.0:
		tmp = y / -1.0
	elif y <= 2.9e+83:
		tmp = -x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3600000.0)
		tmp = 1.0;
	elseif (y <= 8e-110)
		tmp = x;
	elseif (y <= 1.0)
		tmp = Float64(y / -1.0);
	elseif (y <= 2.9e+83)
		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 <= -3600000.0)
		tmp = 1.0;
	elseif (y <= 8e-110)
		tmp = x;
	elseif (y <= 1.0)
		tmp = y / -1.0;
	elseif (y <= 2.9e+83)
		tmp = -x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3600000.0], 1.0, If[LessEqual[y, 8e-110], x, If[LessEqual[y, 1.0], N[(y / -1.0), $MachinePrecision], If[LessEqual[y, 2.9e+83], N[((-x) / y), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.6e6 or 2.89999999999999999e83 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 78.0%

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

   if -3.6e6 < y < 8.0000000000000004e-110

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.7%

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

   if 8.0000000000000004e-110 < y < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 67.2%

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

      1. neg-mul-1 67.2%

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

      2. distribute-neg-frac2 67.2%

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

      3. neg-sub0 67.2%

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

      4. associate--r- 67.2%

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

      5. metadata-eval 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in y around 0 62.0%

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

   if 1 < y < 2.89999999999999999e83

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 60.5%

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

   4. Taylor expanded in y around inf 60.5%

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

      1. associate-*r/ 60.5%

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

      2. neg-mul-1 60.5%

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

   6. Simplified 60.5%

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

Alternative 3: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4200000:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 145000000:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4200000.0)
   (+ 1.0 (/ (- 1.0 x) y))
   (if (<= y 1.15e-107)
     (/ x (- 1.0 y))
     (if (<= y 145000000.0) (/ y (+ y -1.0)) (- 1.0 (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4200000.0) {
		tmp = 1.0 + ((1.0 - x) / y);
	} else if (y <= 1.15e-107) {
		tmp = x / (1.0 - y);
	} else if (y <= 145000000.0) {
		tmp = y / (y + -1.0);
	} else {
		tmp = 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 <= (-4200000.0d0)) then
        tmp = 1.0d0 + ((1.0d0 - x) / y)
    else if (y <= 1.15d-107) then
        tmp = x / (1.0d0 - y)
    else if (y <= 145000000.0d0) then
        tmp = y / (y + (-1.0d0))
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4200000.0) {
		tmp = 1.0 + ((1.0 - x) / y);
	} else if (y <= 1.15e-107) {
		tmp = x / (1.0 - y);
	} else if (y <= 145000000.0) {
		tmp = y / (y + -1.0);
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4200000.0:
		tmp = 1.0 + ((1.0 - x) / y)
	elif y <= 1.15e-107:
		tmp = x / (1.0 - y)
	elif y <= 145000000.0:
		tmp = y / (y + -1.0)
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4200000.0)
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) / y));
	elseif (y <= 1.15e-107)
		tmp = Float64(x / Float64(1.0 - y));
	elseif (y <= 145000000.0)
		tmp = Float64(y / Float64(y + -1.0));
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4200000.0)
		tmp = 1.0 + ((1.0 - x) / y);
	elseif (y <= 1.15e-107)
		tmp = x / (1.0 - y);
	elseif (y <= 145000000.0)
		tmp = y / (y + -1.0);
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4200000.0], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-107], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 145000000.0], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.2e6

   1. Initial program 99.9%

      \[\frac{x - y}{1 - y} \]
   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 -4.2e6 < y < 1.15000000000000002e-107

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.2%

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

   if 1.15000000000000002e-107 < y < 1.45e8

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 68.7%

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

      1. neg-mul-1 68.7%

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

      2. distribute-neg-frac2 68.7%

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

      3. neg-sub0 68.7%

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

      4. associate--r- 68.7%

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

      5. metadata-eval 68.7%

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

   5. Simplified 68.7%

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

   if 1.45e8 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. expm1-log1p-u 0.0%

         \[\leadsto \frac{x - y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - y\right)\right)}} \]

   4. Applied egg-rr 0.0%

      \[\leadsto \frac{x - y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - y\right)\right)}} \]
   5. Step-by-step derivation

      1. expm1-undefine 0.0%

         \[\leadsto \frac{x - y}{\color{blue}{e^{\mathsf{log1p}\left(1 - y\right)} - 1}} \]

      2. sub-neg 0.0%

         \[\leadsto \frac{x - y}{\color{blue}{e^{\mathsf{log1p}\left(1 - y\right)} + \left(-1\right)}} \]

      3. log1p-undefine 0.0%

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

      4. rem-exp-log 100.0%

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

      5. associate-+r- 100.0%

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

      6. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\left(\color{blue}{2} - y\right) + \left(-1\right)} \]

      7. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\left(2 - y\right) + \color{blue}{-1}} \]

   6. Simplified 100.0%

      \[\leadsto \frac{x - y}{\color{blue}{\left(2 - y\right) + -1}} \]

   7. Taylor expanded in y around inf 100.0%

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

      1. neg-mul-1 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in x around 0 100.0%

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

       1. neg-mul-1 100.0%

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

       2. unsub-neg 100.0%

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

   12. Simplified 100.0%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4200000:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 145000000:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -45000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 10^{-107}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 510000:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -45000000.0)
     t_0
     (if (<= y 1e-107)
       (/ x (- 1.0 y))
       (if (<= y 510000.0) (/ y (+ y -1.0)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -45000000.0) {
		tmp = t_0;
	} else if (y <= 1e-107) {
		tmp = x / (1.0 - y);
	} else if (y <= 510000.0) {
		tmp = y / (y + -1.0);
	} 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 <= (-45000000.0d0)) then
        tmp = t_0
    else if (y <= 1d-107) then
        tmp = x / (1.0d0 - y)
    else if (y <= 510000.0d0) then
        tmp = y / (y + (-1.0d0))
    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 <= -45000000.0) {
		tmp = t_0;
	} else if (y <= 1e-107) {
		tmp = x / (1.0 - y);
	} else if (y <= 510000.0) {
		tmp = y / (y + -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -45000000.0:
		tmp = t_0
	elif y <= 1e-107:
		tmp = x / (1.0 - y)
	elif y <= 510000.0:
		tmp = y / (y + -1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -45000000.0)
		tmp = t_0;
	elseif (y <= 1e-107)
		tmp = Float64(x / Float64(1.0 - y));
	elseif (y <= 510000.0)
		tmp = Float64(y / Float64(y + -1.0));
	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 <= -45000000.0)
		tmp = t_0;
	elseif (y <= 1e-107)
		tmp = x / (1.0 - y);
	elseif (y <= 510000.0)
		tmp = y / (y + -1.0);
	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, -45000000.0], t$95$0, If[LessEqual[y, 1e-107], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 510000.0], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5e7 or 5.1e5 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. expm1-log1p-u 51.7%

         \[\leadsto \frac{x - y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - y\right)\right)}} \]

   4. Applied egg-rr 51.7%

      \[\leadsto \frac{x - y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - y\right)\right)}} \]
   5. Step-by-step derivation

      1. expm1-undefine 51.7%

         \[\leadsto \frac{x - y}{\color{blue}{e^{\mathsf{log1p}\left(1 - y\right)} - 1}} \]

      2. sub-neg 51.7%

         \[\leadsto \frac{x - y}{\color{blue}{e^{\mathsf{log1p}\left(1 - y\right)} + \left(-1\right)}} \]

      3. log1p-undefine 51.7%

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

      4. rem-exp-log 100.0%

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

      5. associate-+r- 100.0%

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

      6. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\left(\color{blue}{2} - y\right) + \left(-1\right)} \]

      7. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\left(2 - y\right) + \color{blue}{-1}} \]

   6. Simplified 100.0%

      \[\leadsto \frac{x - y}{\color{blue}{\left(2 - y\right) + -1}} \]

   7. Taylor expanded in y around inf 99.6%

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

      1. neg-mul-1 99.6%

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

   9. Simplified 99.6%

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

   10. Taylor expanded in x around 0 99.7%

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

       1. neg-mul-1 99.7%

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

       2. unsub-neg 99.7%

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

   12. Simplified 99.7%

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

   if -4.5e7 < y < 1e-107

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.2%

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

   if 1e-107 < y < 5.1e5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 68.7%

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

      1. neg-mul-1 68.7%

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

      2. distribute-neg-frac2 68.7%

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

      3. neg-sub0 68.7%

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

      4. associate--r- 68.7%

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

      5. metadata-eval 68.7%

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

   5. Simplified 68.7%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -45000000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 10^{-107}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 510000:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -45000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\frac{y}{-1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -45000000.0)
     t_0
     (if (<= y 1.15e-107) (/ x (- 1.0 y)) (if (<= y 1.0) (/ y -1.0) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -45000000.0) {
		tmp = t_0;
	} else if (y <= 1.15e-107) {
		tmp = x / (1.0 - y);
	} else if (y <= 1.0) {
		tmp = y / -1.0;
	} 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 <= (-45000000.0d0)) then
        tmp = t_0
    else if (y <= 1.15d-107) then
        tmp = x / (1.0d0 - y)
    else if (y <= 1.0d0) then
        tmp = y / (-1.0d0)
    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 <= -45000000.0) {
		tmp = t_0;
	} else if (y <= 1.15e-107) {
		tmp = x / (1.0 - y);
	} else if (y <= 1.0) {
		tmp = y / -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -45000000.0:
		tmp = t_0
	elif y <= 1.15e-107:
		tmp = x / (1.0 - y)
	elif y <= 1.0:
		tmp = y / -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -45000000.0)
		tmp = t_0;
	elseif (y <= 1.15e-107)
		tmp = Float64(x / Float64(1.0 - y));
	elseif (y <= 1.0)
		tmp = Float64(y / -1.0);
	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 <= -45000000.0)
		tmp = t_0;
	elseif (y <= 1.15e-107)
		tmp = x / (1.0 - y);
	elseif (y <= 1.0)
		tmp = y / -1.0;
	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, -45000000.0], t$95$0, If[LessEqual[y, 1.15e-107], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(y / -1.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5e7 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. expm1-log1p-u 51.3%

         \[\leadsto \frac{x - y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - y\right)\right)}} \]

   4. Applied egg-rr 51.3%

      \[\leadsto \frac{x - y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - y\right)\right)}} \]
   5. Step-by-step derivation

      1. expm1-undefine 51.3%

         \[\leadsto \frac{x - y}{\color{blue}{e^{\mathsf{log1p}\left(1 - y\right)} - 1}} \]

      2. sub-neg 51.3%

         \[\leadsto \frac{x - y}{\color{blue}{e^{\mathsf{log1p}\left(1 - y\right)} + \left(-1\right)}} \]

      3. log1p-undefine 51.3%

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

      4. rem-exp-log 100.0%

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

      5. associate-+r- 100.0%

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

      6. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\left(\color{blue}{2} - y\right) + \left(-1\right)} \]

      7. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\left(2 - y\right) + \color{blue}{-1}} \]

   6. Simplified 100.0%

      \[\leadsto \frac{x - y}{\color{blue}{\left(2 - y\right) + -1}} \]

   7. Taylor expanded in y around inf 99.1%

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

      1. neg-mul-1 99.1%

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

   9. Simplified 99.1%

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

   10. Taylor expanded in x around 0 99.2%

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

       1. neg-mul-1 99.2%

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

       2. unsub-neg 99.2%

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

   12. Simplified 99.2%

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

   if -4.5e7 < y < 1.15000000000000002e-107

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.2%

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

   if 1.15000000000000002e-107 < y < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 67.2%

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

      1. neg-mul-1 67.2%

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

      2. distribute-neg-frac2 67.2%

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

      3. neg-sub0 67.2%

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

      4. associate--r- 67.2%

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

      5. metadata-eval 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in y around 0 62.0%

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

Alternative 6: 84.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -0.2:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\frac{y}{-1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -0.2)
     t_0
     (if (<= y 1.15e-107) x (if (<= y 1.0) (/ y -1.0) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -0.2) {
		tmp = t_0;
	} else if (y <= 1.15e-107) {
		tmp = x;
	} else if (y <= 1.0) {
		tmp = y / -1.0;
	} 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 <= (-0.2d0)) then
        tmp = t_0
    else if (y <= 1.15d-107) then
        tmp = x
    else if (y <= 1.0d0) then
        tmp = y / (-1.0d0)
    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 <= -0.2) {
		tmp = t_0;
	} else if (y <= 1.15e-107) {
		tmp = x;
	} else if (y <= 1.0) {
		tmp = y / -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -0.2:
		tmp = t_0
	elif y <= 1.15e-107:
		tmp = x
	elif y <= 1.0:
		tmp = y / -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -0.2)
		tmp = t_0;
	elseif (y <= 1.15e-107)
		tmp = x;
	elseif (y <= 1.0)
		tmp = Float64(y / -1.0);
	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 <= -0.2)
		tmp = t_0;
	elseif (y <= 1.15e-107)
		tmp = x;
	elseif (y <= 1.0)
		tmp = y / -1.0;
	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, -0.2], t$95$0, If[LessEqual[y, 1.15e-107], x, If[LessEqual[y, 1.0], N[(y / -1.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.20000000000000001 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. expm1-log1p-u 51.7%

         \[\leadsto \frac{x - y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - y\right)\right)}} \]

   4. Applied egg-rr 51.7%

      \[\leadsto \frac{x - y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - y\right)\right)}} \]
   5. Step-by-step derivation

      1. expm1-undefine 51.7%

         \[\leadsto \frac{x - y}{\color{blue}{e^{\mathsf{log1p}\left(1 - y\right)} - 1}} \]

      2. sub-neg 51.7%

         \[\leadsto \frac{x - y}{\color{blue}{e^{\mathsf{log1p}\left(1 - y\right)} + \left(-1\right)}} \]

      3. log1p-undefine 51.7%

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

      4. rem-exp-log 100.0%

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

      5. associate-+r- 100.0%

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

      6. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\left(\color{blue}{2} - y\right) + \left(-1\right)} \]

      7. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\left(2 - y\right) + \color{blue}{-1}} \]

   6. Simplified 100.0%

      \[\leadsto \frac{x - y}{\color{blue}{\left(2 - y\right) + -1}} \]

   7. Taylor expanded in y around inf 98.8%

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

      1. neg-mul-1 98.8%

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

   9. Simplified 98.8%

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

   10. Taylor expanded in x around 0 98.8%

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

       1. neg-mul-1 98.8%

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

       2. unsub-neg 98.8%

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

   12. Simplified 98.8%

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

   if -0.20000000000000001 < y < 1.15000000000000002e-107

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.4%

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

   if 1.15000000000000002e-107 < y < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 67.2%

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

      1. neg-mul-1 67.2%

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

      2. distribute-neg-frac2 67.2%

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

      3. neg-sub0 67.2%

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

      4. associate--r- 67.2%

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

      5. metadata-eval 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in y around 0 62.0%

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

Alternative 7: 73.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3600000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.0033:\\ \;\;\;\;\frac{y}{-1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3600000.0)
   1.0
   (if (<= y 3.3e-108) x (if (<= y 0.0033) (/ y -1.0) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3600000.0) {
		tmp = 1.0;
	} else if (y <= 3.3e-108) {
		tmp = x;
	} else if (y <= 0.0033) {
		tmp = 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 <= (-3600000.0d0)) then
        tmp = 1.0d0
    else if (y <= 3.3d-108) then
        tmp = x
    else if (y <= 0.0033d0) then
        tmp = 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 <= -3600000.0) {
		tmp = 1.0;
	} else if (y <= 3.3e-108) {
		tmp = x;
	} else if (y <= 0.0033) {
		tmp = y / -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3600000.0:
		tmp = 1.0
	elif y <= 3.3e-108:
		tmp = x
	elif y <= 0.0033:
		tmp = y / -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3600000.0)
		tmp = 1.0;
	elseif (y <= 3.3e-108)
		tmp = x;
	elseif (y <= 0.0033)
		tmp = Float64(y / -1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3600000.0)
		tmp = 1.0;
	elseif (y <= 3.3e-108)
		tmp = x;
	elseif (y <= 0.0033)
		tmp = y / -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3600000.0], 1.0, If[LessEqual[y, 3.3e-108], x, If[LessEqual[y, 0.0033], N[(y / -1.0), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e6 or 0.0033 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.0%

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

   if -3.6e6 < y < 3.3000000000000002e-108

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.7%

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

   if 3.3000000000000002e-108 < y < 0.0033

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 70.5%

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

      1. neg-mul-1 70.5%

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

      2. distribute-neg-frac2 70.5%

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

      3. neg-sub0 70.5%

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

      4. associate--r- 70.5%

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

      5. metadata-eval 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in y around 0 65.1%

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

Alternative 8: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3600000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3600000.0) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3600000.0) {
		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 <= (-3600000.0d0)) 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 <= -3600000.0) {
		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 <= -3600000.0:
		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 <= -3600000.0)
		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 <= -3600000.0)
		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, -3600000.0], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e6 or 1 < 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 -3.6e6 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.9%

      \[\leadsto \color{blue}{x} \]
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 38.9%

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

Reproduce

herbie shell --seed 2024180 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))