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

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

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. Final simplification 100.0%

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

Alternative 2: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - y}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+27}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-39}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-8}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+22}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 y))))
   (if (<= y -6.5e+27)
     1.0
     (if (<= y 6.6e-39)
       t_0
       (if (<= y 3e-8) (- y) (if (<= y 7.4e+22) t_0 1.0))))))

C

double code(double x, double y) {
	double t_0 = x / (1.0 - y);
	double tmp;
	if (y <= -6.5e+27) {
		tmp = 1.0;
	} else if (y <= 6.6e-39) {
		tmp = t_0;
	} else if (y <= 3e-8) {
		tmp = -y;
	} else if (y <= 7.4e+22) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x / (1.0d0 - y)
    if (y <= (-6.5d+27)) then
        tmp = 1.0d0
    else if (y <= 6.6d-39) then
        tmp = t_0
    else if (y <= 3d-8) then
        tmp = -y
    else if (y <= 7.4d+22) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (1.0 - y);
	double tmp;
	if (y <= -6.5e+27) {
		tmp = 1.0;
	} else if (y <= 6.6e-39) {
		tmp = t_0;
	} else if (y <= 3e-8) {
		tmp = -y;
	} else if (y <= 7.4e+22) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (1.0 - y)
	tmp = 0
	if y <= -6.5e+27:
		tmp = 1.0
	elif y <= 6.6e-39:
		tmp = t_0
	elif y <= 3e-8:
		tmp = -y
	elif y <= 7.4e+22:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(1.0 - y))
	tmp = 0.0
	if (y <= -6.5e+27)
		tmp = 1.0;
	elseif (y <= 6.6e-39)
		tmp = t_0;
	elseif (y <= 3e-8)
		tmp = Float64(-y);
	elseif (y <= 7.4e+22)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (1.0 - y);
	tmp = 0.0;
	if (y <= -6.5e+27)
		tmp = 1.0;
	elseif (y <= 6.6e-39)
		tmp = t_0;
	elseif (y <= 3e-8)
		tmp = -y;
	elseif (y <= 7.4e+22)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+27], 1.0, If[LessEqual[y, 6.6e-39], t$95$0, If[LessEqual[y, 3e-8], (-y), If[LessEqual[y, 7.4e+22], t$95$0, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5000000000000005e27 or 7.3999999999999996e22 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.9%

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

   if -6.5000000000000005e27 < y < 6.5999999999999997e-39 or 2.99999999999999973e-8 < y < 7.3999999999999996e22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.5%

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

   if 6.5999999999999997e-39 < y < 2.99999999999999973e-8

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 87.6%

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

      1. neg-mul-1 87.6%

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

      2. distribute-neg-frac2 87.6%

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

      3. neg-sub0 87.6%

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

      4. associate--r- 87.6%

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

      5. metadata-eval 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in y around 0 81.5%

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

      1. neg-mul-1 81.5%

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

   8. Simplified 81.5%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+27}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-8}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x + -1}{y}\\ \mathbf{if}\;y \leq -1050:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 15000:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ (+ x -1.0) y))))
   (if (<= y -1050.0)
     t_0
     (if (<= y 1.15e-37)
       (/ x (- 1.0 y))
       (if (<= y 15000.0) (/ y (+ y -1.0)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - ((x + -1.0) / y);
	double tmp;
	if (y <= -1050.0) {
		tmp = t_0;
	} else if (y <= 1.15e-37) {
		tmp = x / (1.0 - y);
	} else if (y <= 15000.0) {
		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 + (-1.0d0)) / y)
    if (y <= (-1050.0d0)) then
        tmp = t_0
    else if (y <= 1.15d-37) then
        tmp = x / (1.0d0 - y)
    else if (y <= 15000.0d0) 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 + -1.0) / y);
	double tmp;
	if (y <= -1050.0) {
		tmp = t_0;
	} else if (y <= 1.15e-37) {
		tmp = x / (1.0 - y);
	} else if (y <= 15000.0) {
		tmp = y / (y + -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - ((x + -1.0) / y)
	tmp = 0
	if y <= -1050.0:
		tmp = t_0
	elif y <= 1.15e-37:
		tmp = x / (1.0 - y)
	elif y <= 15000.0:
		tmp = y / (y + -1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(Float64(x + -1.0) / y))
	tmp = 0.0
	if (y <= -1050.0)
		tmp = t_0;
	elseif (y <= 1.15e-37)
		tmp = Float64(x / Float64(1.0 - y));
	elseif (y <= 15000.0)
		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 + -1.0) / y);
	tmp = 0.0;
	if (y <= -1050.0)
		tmp = t_0;
	elseif (y <= 1.15e-37)
		tmp = x / (1.0 - y);
	elseif (y <= 15000.0)
		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[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1050.0], t$95$0, If[LessEqual[y, 1.15e-37], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 15000.0], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1050 or 15000 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.6%

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

      1. +-commutative 99.6%

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

      2. mul-1-neg 99.6%

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

      3. unsub-neg 99.6%

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

      4. div-sub 99.6%

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

   5. Simplified 99.6%

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

   if -1050 < y < 1.15e-37

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.9%

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

   if 1.15e-37 < y < 15000

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.0%

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

      1. neg-mul-1 74.0%

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

      2. distribute-neg-frac2 74.0%

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

      3. neg-sub0 74.0%

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

      4. associate--r- 74.0%

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

      5. metadata-eval 74.0%

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

   5. Simplified 74.0%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1050:\\ \;\;\;\;1 - \frac{x + -1}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 15000:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x + -1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.3) 1.0 (if (<= y 3e-43) x (if (<= y 1.0) (- y) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.3) {
		tmp = 1.0;
	} else if (y <= 3e-43) {
		tmp = x;
	} else if (y <= 1.0) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.3d0)) then
        tmp = 1.0d0
    else if (y <= 3d-43) then
        tmp = x
    else if (y <= 1.0d0) then
        tmp = -y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.3) {
		tmp = 1.0;
	} else if (y <= 3e-43) {
		tmp = x;
	} else if (y <= 1.0) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.3:
		tmp = 1.0
	elif y <= 3e-43:
		tmp = x
	elif y <= 1.0:
		tmp = -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.3)
		tmp = 1.0;
	elseif (y <= 3e-43)
		tmp = x;
	elseif (y <= 1.0)
		tmp = Float64(-y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.3)
		tmp = 1.0;
	elseif (y <= 3e-43)
		tmp = x;
	elseif (y <= 1.0)
		tmp = -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.3], 1.0, If[LessEqual[y, 3e-43], x, If[LessEqual[y, 1.0], (-y), 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.30000000000000004 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 -1.30000000000000004 < y < 3.00000000000000003e-43

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.4%

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

   if 3.00000000000000003e-43 < y < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 71.4%

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

      1. neg-mul-1 71.4%

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

      2. distribute-neg-frac2 71.4%

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

      3. neg-sub0 71.4%

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

      4. associate--r- 71.4%

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

      5. metadata-eval 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in y around 0 66.5%

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

      1. neg-mul-1 66.5%

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

   8. Simplified 66.5%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.25:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-42}:\\ \;\;\;\;x + x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.25)
   1.0
   (if (<= y 7e-42) (+ x (* x y)) (if (<= y 1.0) (- y) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.25) {
		tmp = 1.0;
	} else if (y <= 7e-42) {
		tmp = x + (x * y);
	} else if (y <= 1.0) {
		tmp = -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 <= (-0.25d0)) then
        tmp = 1.0d0
    else if (y <= 7d-42) then
        tmp = x + (x * y)
    else if (y <= 1.0d0) then
        tmp = -y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -0.25) {
		tmp = 1.0;
	} else if (y <= 7e-42) {
		tmp = x + (x * y);
	} else if (y <= 1.0) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.25:
		tmp = 1.0
	elif y <= 7e-42:
		tmp = x + (x * y)
	elif y <= 1.0:
		tmp = -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.25)
		tmp = 1.0;
	elseif (y <= 7e-42)
		tmp = Float64(x + Float64(x * y));
	elseif (y <= 1.0)
		tmp = Float64(-y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.25)
		tmp = 1.0;
	elseif (y <= 7e-42)
		tmp = x + (x * y);
	elseif (y <= 1.0)
		tmp = -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.25], 1.0, If[LessEqual[y, 7e-42], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], (-y), 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.25 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 -0.25 < y < 7.0000000000000004e-42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.9%

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

   4. Taylor expanded in y around 0 79.6%

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

      1. *-commutative 79.6%

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

   6. Simplified 79.6%

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

   if 7.0000000000000004e-42 < y < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 71.4%

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

      1. neg-mul-1 71.4%

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

      2. distribute-neg-frac2 71.4%

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

      3. neg-sub0 71.4%

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

      4. associate--r- 71.4%

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

      5. metadata-eval 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in y around 0 66.5%

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

      1. neg-mul-1 66.5%

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

   8. Simplified 66.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.25:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-42}:\\ \;\;\;\;x + x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.5% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.3%

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

      1. +-commutative 99.3%

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

      2. mul-1-neg 99.3%

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

      3. unsub-neg 99.3%

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

      4. div-sub 99.3%

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

   5. Simplified 99.3%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.4%

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

      1. mul-1-neg 98.4%

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

      2. unsub-neg 98.4%

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

      3. mul-1-neg 98.4%

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

      4. unsub-neg 98.4%

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

   5. Simplified 98.4%

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

4. Final simplification 98.9%

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

Alternative 7: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-39} \lor \neg \left(y \leq 6.2 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -9.5e-39) (not (<= y 6.2e-38))) (/ y (+ y -1.0)) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -9.5e-39) || !(y <= 6.2e-38)) {
		tmp = y / (y + -1.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-9.5d-39)) .or. (.not. (y <= 6.2d-38))) then
        tmp = y / (y + (-1.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -9.5e-39) || !(y <= 6.2e-38)) {
		tmp = y / (y + -1.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -9.5e-39) or not (y <= 6.2e-38):
		tmp = y / (y + -1.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -9.5e-39) || !(y <= 6.2e-38))
		tmp = Float64(y / Float64(y + -1.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -9.5e-39) || ~((y <= 6.2e-38)))
		tmp = y / (y + -1.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -9.5e-39], N[Not[LessEqual[y, 6.2e-38]], $MachinePrecision]], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999999e-39 or 6.19999999999999966e-38 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.0%

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

      1. neg-mul-1 78.0%

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

      2. distribute-neg-frac2 78.0%

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

      3. neg-sub0 78.0%

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

      4. associate--r- 78.0%

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

      5. metadata-eval 78.0%

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

   5. Simplified 78.0%

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

   if -9.4999999999999999e-39 < y < 6.19999999999999966e-38

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.9%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-39} \lor \neg \left(y \leq 6.2 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.49:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -0.49) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.49) {
		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 <= (-0.49d0)) 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 <= -0.49) {
		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 <= -0.49:
		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 <= -0.49)
		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 <= -0.49)
		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, -0.49], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -0.48999999999999999 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 -0.48999999999999999 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.5%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.49:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. 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. Final simplification 43.1%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024041 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))