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

Percentage Accurate: 100.0% → 100.0%

Time: 7.9s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

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: 86.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-6}:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3e+20)
   1.0
   (if (<= y -1.28e-5)
     (/ x (- 1.0 y))
     (if (<= y 4.2e-6) (- x y) (/ y (+ y -1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3e+20) {
		tmp = 1.0;
	} else if (y <= -1.28e-5) {
		tmp = x / (1.0 - y);
	} else if (y <= 4.2e-6) {
		tmp = x - y;
	} 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) :: tmp
    if (y <= (-3d+20)) then
        tmp = 1.0d0
    else if (y <= (-1.28d-5)) then
        tmp = x / (1.0d0 - y)
    else if (y <= 4.2d-6) then
        tmp = x - y
    else
        tmp = y / (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3e+20) {
		tmp = 1.0;
	} else if (y <= -1.28e-5) {
		tmp = x / (1.0 - y);
	} else if (y <= 4.2e-6) {
		tmp = x - y;
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3e+20:
		tmp = 1.0
	elif y <= -1.28e-5:
		tmp = x / (1.0 - y)
	elif y <= 4.2e-6:
		tmp = x - y
	else:
		tmp = y / (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3e+20)
		tmp = 1.0;
	elseif (y <= -1.28e-5)
		tmp = Float64(x / Float64(1.0 - y));
	elseif (y <= 4.2e-6)
		tmp = Float64(x - y);
	else
		tmp = Float64(y / Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3e+20)
		tmp = 1.0;
	elseif (y <= -1.28e-5)
		tmp = x / (1.0 - y);
	elseif (y <= 4.2e-6)
		tmp = x - y;
	else
		tmp = y / (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3e+20], 1.0, If[LessEqual[y, -1.28e-5], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-6], N[(x - y), $MachinePrecision], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3e20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 90.1%

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

   if -3e20 < y < -1.2799999999999999e-5

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 87.5%

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

   if -1.2799999999999999e-5 < y < 4.1999999999999996e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. associate-*r* 100.0%

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

      4. neg-mul-1 100.0%

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

      5. mul-1-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. sub-neg 100.0%

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

      8. sub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 99.3%

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

   7. Taylor expanded in y around 0 97.8%

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

      1. neg-mul-1 97.8%

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

      2. unsub-neg 97.8%

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

   9. Simplified 97.8%

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

   if 4.1999999999999996e-6 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.2%

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

      1. neg-mul-1 73.2%

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

      2. distribute-neg-frac2 73.2%

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

      3. neg-sub0 73.2%

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

      4. associate--r- 73.2%

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

      5. metadata-eval 73.2%

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

   5. Simplified 73.2%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-6}:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.6e+20)
   1.0
   (if (<= y -1.4e-6) (/ x (- 1.0 y)) (if (<= y 1.0) (- x y) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.6e+20) {
		tmp = 1.0;
	} else if (y <= -1.4e-6) {
		tmp = x / (1.0 - y);
	} else if (y <= 1.0) {
		tmp = x - y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.6d+20)) then
        tmp = 1.0d0
    else if (y <= (-1.4d-6)) then
        tmp = x / (1.0d0 - y)
    else if (y <= 1.0d0) then
        tmp = x - y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.6e+20) {
		tmp = 1.0;
	} else if (y <= -1.4e-6) {
		tmp = x / (1.0 - y);
	} else if (y <= 1.0) {
		tmp = x - y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.6e+20:
		tmp = 1.0
	elif y <= -1.4e-6:
		tmp = x / (1.0 - y)
	elif y <= 1.0:
		tmp = x - y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.6e+20)
		tmp = 1.0;
	elseif (y <= -1.4e-6)
		tmp = Float64(x / Float64(1.0 - y));
	elseif (y <= 1.0)
		tmp = Float64(x - y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.6e+20)
		tmp = 1.0;
	elseif (y <= -1.4e-6)
		tmp = x / (1.0 - y);
	elseif (y <= 1.0)
		tmp = x - y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.6e+20], 1.0, If[LessEqual[y, -1.4e-6], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(x - y), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e20 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.7%

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

   if -3.6e20 < y < -1.39999999999999994e-6

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 87.5%

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

   if -1.39999999999999994e-6 < y < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. associate-*r* 100.0%

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

      4. neg-mul-1 100.0%

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

      5. mul-1-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. sub-neg 100.0%

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

      8. sub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 99.3%

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

   7. Taylor expanded in y around 0 97.8%

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

      1. neg-mul-1 97.8%

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

      2. unsub-neg 97.8%

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

   9. Simplified 97.8%

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

Alternative 4: 98.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.8 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;\frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(-1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -0.8) (not (<= y 1.0))) (/ (- y x) y) (+ x (* y (- -1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -0.8) || !(y <= 1.0)) {
		tmp = (y - x) / y;
	} else {
		tmp = x + (y * (-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 <= (-0.8d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = (y - x) / y
    else
        tmp = x + (y * ((-1.0d0) - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -0.8) || !(y <= 1.0)) {
		tmp = (y - x) / y;
	} else {
		tmp = x + (y * (-1.0 - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -0.8) or not (y <= 1.0):
		tmp = (y - x) / y
	else:
		tmp = x + (y * (-1.0 - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -0.8) || !(y <= 1.0))
		tmp = Float64(Float64(y - x) / y);
	else
		tmp = Float64(x + Float64(y * Float64(-1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -0.8) || ~((y <= 1.0)))
		tmp = (y - x) / y;
	else
		tmp = x + (y * (-1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -0.8], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision], N[(x + N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.80000000000000004 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 40.5%

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

   4. Applied egg-rr 40.5%

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

      1. expm1-undefine 40.5%

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

      2. sub-neg 40.5%

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

      3. log1p-undefine 40.5%

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

      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 98.4%

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

      1. mul-1-neg 98.4%

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

   9. Simplified 98.4%

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

   10. Taylor expanded in y around 0 98.4%

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

       1. neg-mul-1 98.4%

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

       2. unsub-neg 98.4%

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

   12. Simplified 98.4%

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

   if -0.80000000000000004 < y < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.1%

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

      1. mul-1-neg 99.1%

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

      2. associate-*r* 99.1%

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

      3. neg-mul-1 99.1%

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

      4. mul-1-neg 99.1%

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

      5. sub-neg 99.1%

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

      6. sub-neg 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in x around 0 98.0%

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

      1. sub-neg 98.0%

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

      2. mul-1-neg 98.0%

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

      3. distribute-neg-in 98.0%

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

      4. +-commutative 98.0%

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

      5. distribute-neg-in 98.0%

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

      6. metadata-eval 98.0%

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

      7. sub-neg 98.0%

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

   8. Simplified 98.0%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.8 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;\frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(-1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.000235:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-82}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.000235) 1.0 (if (<= y -2.9e-82) (- y) (if (<= y 1.0) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.000235) {
		tmp = 1.0;
	} else if (y <= -2.9e-82) {
		tmp = -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 <= (-0.000235d0)) then
        tmp = 1.0d0
    else if (y <= (-2.9d-82)) then
        tmp = -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 <= -0.000235) {
		tmp = 1.0;
	} else if (y <= -2.9e-82) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.000235:
		tmp = 1.0
	elif y <= -2.9e-82:
		tmp = -y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.000235)
		tmp = 1.0;
	elseif (y <= -2.9e-82)
		tmp = 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 <= -0.000235)
		tmp = 1.0;
	elseif (y <= -2.9e-82)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.000235], 1.0, If[LessEqual[y, -2.9e-82], (-y), If[LessEqual[y, 1.0], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.34999999999999993e-4 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 75.9%

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

   if -2.34999999999999993e-4 < y < -2.89999999999999977e-82

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 69.4%

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

      1. neg-mul-1 69.4%

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

      2. distribute-neg-frac2 69.4%

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

      3. neg-sub0 69.4%

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

      4. associate--r- 69.4%

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

      5. metadata-eval 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in y around 0 62.3%

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

      1. neg-mul-1 62.3%

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

   8. Simplified 62.3%

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

   if -2.89999999999999977e-82 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.6%

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

Alternative 6: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = (y - x) / y
    else
        tmp = x - y
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision], N[(x - y), $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. Step-by-step derivation

      1. expm1-log1p-u 40.5%

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

   4. Applied egg-rr 40.5%

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

      1. expm1-undefine 40.5%

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

      2. sub-neg 40.5%

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

      3. log1p-undefine 40.5%

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

      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 98.4%

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

      1. mul-1-neg 98.4%

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

   9. Simplified 98.4%

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

   10. Taylor expanded in y around 0 98.4%

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

       1. neg-mul-1 98.4%

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

       2. unsub-neg 98.4%

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

   12. Simplified 98.4%

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

   if -1 < y < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.4%

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

      1. mul-1-neg 99.4%

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

      2. mul-1-neg 99.4%

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

      3. associate-*r* 99.4%

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

      4. neg-mul-1 99.4%

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

      5. mul-1-neg 99.4%

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

      6. sub-neg 99.4%

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

      7. sub-neg 99.4%

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

      8. sub-neg 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in x around 0 98.2%

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

   7. Taylor expanded in y around 0 96.7%

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

      1. neg-mul-1 96.7%

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

      2. unsub-neg 96.7%

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

   9. Simplified 96.7%

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

4. Final simplification 97.6%

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

Alternative 7: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1200000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1200000.0) 1.0 (if (<= y 1.0) (- x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1200000.0) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x - y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1200000.0d0)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x - y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1200000.0) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x - y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1200000.0:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x - y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1200000.0)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = Float64(x - y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1200000.0)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x - y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1200000.0], 1.0, If[LessEqual[y, 1.0], N[(x - y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e6 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 78.1%

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

   if -1.2e6 < y < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 97.8%

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

      1. mul-1-neg 97.8%

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

      2. mul-1-neg 97.8%

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

      3. associate-*r* 97.8%

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

      4. neg-mul-1 97.8%

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

      5. mul-1-neg 97.8%

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

      6. sub-neg 97.8%

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

      7. sub-neg 97.8%

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

      8. sub-neg 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in x around 0 96.8%

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

   7. Taylor expanded in y around 0 95.3%

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

      1. neg-mul-1 95.3%

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

      2. unsub-neg 95.3%

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

   9. Simplified 95.3%

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

Alternative 8: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1200000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1200000.0) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1200000.0) {
		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 <= (-1200000.0d0)) 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 <= -1200000.0) {
		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 <= -1200000.0:
		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 <= -1200000.0)
		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 <= -1200000.0)
		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, -1200000.0], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e6 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 78.1%

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

   if -1.2e6 < y < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.5%

      \[\leadsto \color{blue}{x} \]
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 43.1%

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

Reproduce

herbie shell --seed 2024177 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))