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

Percentage Accurate: 100.0% → 100.0%

Time: 6.8s

Alternatives: 8

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: 73.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - y}\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+58}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{+30}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-5} \lor \neg \left(x \leq 1.62 \cdot 10^{-46}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 y))))
   (if (<= x -1.7e+58)
     t_0
     (if (<= x -9.8e+30)
       1.0
       (if (or (<= x -4.8e-5) (not (<= x 1.62e-46))) t_0 (/ y (+ y -1.0)))))))

C

double code(double x, double y) {
	double t_0 = x / (1.0 - y);
	double tmp;
	if (x <= -1.7e+58) {
		tmp = t_0;
	} else if (x <= -9.8e+30) {
		tmp = 1.0;
	} else if ((x <= -4.8e-5) || !(x <= 1.62e-46)) {
		tmp = t_0;
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (1.0d0 - y)
    if (x <= (-1.7d+58)) then
        tmp = t_0
    else if (x <= (-9.8d+30)) then
        tmp = 1.0d0
    else if ((x <= (-4.8d-5)) .or. (.not. (x <= 1.62d-46))) then
        tmp = t_0
    else
        tmp = y / (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (1.0 - y);
	double tmp;
	if (x <= -1.7e+58) {
		tmp = t_0;
	} else if (x <= -9.8e+30) {
		tmp = 1.0;
	} else if ((x <= -4.8e-5) || !(x <= 1.62e-46)) {
		tmp = t_0;
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (1.0 - y)
	tmp = 0
	if x <= -1.7e+58:
		tmp = t_0
	elif x <= -9.8e+30:
		tmp = 1.0
	elif (x <= -4.8e-5) or not (x <= 1.62e-46):
		tmp = t_0
	else:
		tmp = y / (y + -1.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(1.0 - y))
	tmp = 0.0
	if (x <= -1.7e+58)
		tmp = t_0;
	elseif (x <= -9.8e+30)
		tmp = 1.0;
	elseif ((x <= -4.8e-5) || !(x <= 1.62e-46))
		tmp = t_0;
	else
		tmp = Float64(y / Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (1.0 - y);
	tmp = 0.0;
	if (x <= -1.7e+58)
		tmp = t_0;
	elseif (x <= -9.8e+30)
		tmp = 1.0;
	elseif ((x <= -4.8e-5) || ~((x <= 1.62e-46)))
		tmp = t_0;
	else
		tmp = y / (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e+58], t$95$0, If[LessEqual[x, -9.8e+30], 1.0, If[Or[LessEqual[x, -4.8e-5], N[Not[LessEqual[x, 1.62e-46]], $MachinePrecision]], t$95$0, N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7e58 or -9.79999999999999969e30 < x < -4.8000000000000001e-5 or 1.6200000000000001e-46 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.7%

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

   if -1.7e58 < x < -9.79999999999999969e30

   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 -4.8000000000000001e-5 < x < 1.6200000000000001e-46

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.4%

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

      1. neg-mul-1 82.4%

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

      2. distribute-neg-frac2 82.4%

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

      3. neg-sub0 82.4%

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

      4. associate--r- 82.4%

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

      5. metadata-eval 82.4%

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

   5. Simplified 82.4%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{+30}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-5} \lor \neg \left(x \leq 1.62 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - y}\\ \mathbf{if}\;x \leq -2 \cdot 10^{+56}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+30}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \frac{1}{1 - y}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-59}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 y))))
   (if (<= x -2e+56)
     t_0
     (if (<= x -6.5e+30)
       1.0
       (if (<= x -3.1e-9)
         (* x (/ 1.0 (- 1.0 y)))
         (if (<= x 2.4e-59) (/ y (+ y -1.0)) t_0))))))

C

double code(double x, double y) {
	double t_0 = x / (1.0 - y);
	double tmp;
	if (x <= -2e+56) {
		tmp = t_0;
	} else if (x <= -6.5e+30) {
		tmp = 1.0;
	} else if (x <= -3.1e-9) {
		tmp = x * (1.0 / (1.0 - y));
	} else if (x <= 2.4e-59) {
		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 = x / (1.0d0 - y)
    if (x <= (-2d+56)) then
        tmp = t_0
    else if (x <= (-6.5d+30)) then
        tmp = 1.0d0
    else if (x <= (-3.1d-9)) then
        tmp = x * (1.0d0 / (1.0d0 - y))
    else if (x <= 2.4d-59) 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 = x / (1.0 - y);
	double tmp;
	if (x <= -2e+56) {
		tmp = t_0;
	} else if (x <= -6.5e+30) {
		tmp = 1.0;
	} else if (x <= -3.1e-9) {
		tmp = x * (1.0 / (1.0 - y));
	} else if (x <= 2.4e-59) {
		tmp = y / (y + -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (1.0 - y)
	tmp = 0
	if x <= -2e+56:
		tmp = t_0
	elif x <= -6.5e+30:
		tmp = 1.0
	elif x <= -3.1e-9:
		tmp = x * (1.0 / (1.0 - y))
	elif x <= 2.4e-59:
		tmp = y / (y + -1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(1.0 - y))
	tmp = 0.0
	if (x <= -2e+56)
		tmp = t_0;
	elseif (x <= -6.5e+30)
		tmp = 1.0;
	elseif (x <= -3.1e-9)
		tmp = Float64(x * Float64(1.0 / Float64(1.0 - y)));
	elseif (x <= 2.4e-59)
		tmp = Float64(y / Float64(y + -1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (1.0 - y);
	tmp = 0.0;
	if (x <= -2e+56)
		tmp = t_0;
	elseif (x <= -6.5e+30)
		tmp = 1.0;
	elseif (x <= -3.1e-9)
		tmp = x * (1.0 / (1.0 - y));
	elseif (x <= 2.4e-59)
		tmp = y / (y + -1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+56], t$95$0, If[LessEqual[x, -6.5e+30], 1.0, If[LessEqual[x, -3.1e-9], N[(x * N[(1.0 / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-59], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.00000000000000018e56 or 2.40000000000000015e-59 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.1%

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

   if -2.00000000000000018e56 < x < -6.5e30

   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 -6.5e30 < x < -3.10000000000000005e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.3%

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

      1. clear-num 86.0%

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

      2. associate-/r/ 86.3%

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

   5. Applied egg-rr 86.3%

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

   if -3.10000000000000005e-9 < x < 2.40000000000000015e-59

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.4%

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

      1. neg-mul-1 82.4%

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

      2. distribute-neg-frac2 82.4%

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

      3. neg-sub0 82.4%

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

      4. associate--r- 82.4%

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

      5. metadata-eval 82.4%

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

   5. Simplified 82.4%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+30}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \frac{1}{1 - y}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-59}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - y}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-61}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-114}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+45}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 y))))
   (if (<= y -1.4e+20)
     1.0
     (if (<= y -2.1e-61)
       t_0
       (if (<= y -1.3e-114) (- y) (if (<= y 4.4e+45) t_0 1.0))))))

C

double code(double x, double y) {
	double t_0 = x / (1.0 - y);
	double tmp;
	if (y <= -1.4e+20) {
		tmp = 1.0;
	} else if (y <= -2.1e-61) {
		tmp = t_0;
	} else if (y <= -1.3e-114) {
		tmp = -y;
	} else if (y <= 4.4e+45) {
		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 <= (-1.4d+20)) then
        tmp = 1.0d0
    else if (y <= (-2.1d-61)) then
        tmp = t_0
    else if (y <= (-1.3d-114)) then
        tmp = -y
    else if (y <= 4.4d+45) 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 <= -1.4e+20) {
		tmp = 1.0;
	} else if (y <= -2.1e-61) {
		tmp = t_0;
	} else if (y <= -1.3e-114) {
		tmp = -y;
	} else if (y <= 4.4e+45) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (1.0 - y)
	tmp = 0
	if y <= -1.4e+20:
		tmp = 1.0
	elif y <= -2.1e-61:
		tmp = t_0
	elif y <= -1.3e-114:
		tmp = -y
	elif y <= 4.4e+45:
		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 <= -1.4e+20)
		tmp = 1.0;
	elseif (y <= -2.1e-61)
		tmp = t_0;
	elseif (y <= -1.3e-114)
		tmp = Float64(-y);
	elseif (y <= 4.4e+45)
		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 <= -1.4e+20)
		tmp = 1.0;
	elseif (y <= -2.1e-61)
		tmp = t_0;
	elseif (y <= -1.3e-114)
		tmp = -y;
	elseif (y <= 4.4e+45)
		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, -1.4e+20], 1.0, If[LessEqual[y, -2.1e-61], t$95$0, If[LessEqual[y, -1.3e-114], (-y), If[LessEqual[y, 4.4e+45], t$95$0, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e20 or 4.4000000000000001e45 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 82.0%

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

   if -1.4e20 < y < -2.0999999999999999e-61 or -1.30000000000000007e-114 < y < 4.4000000000000001e45

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.6%

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

   if -2.0999999999999999e-61 < y < -1.30000000000000007e-114

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.9%

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

      1. neg-mul-1 73.9%

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

      2. distribute-neg-frac2 73.9%

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

      3. neg-sub0 73.9%

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

      4. associate--r- 73.9%

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

      5. metadata-eval 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in y around 0 73.9%

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

      1. neg-mul-1 73.9%

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

   8. Simplified 73.9%

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

Alternative 5: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-114}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.45e-6)
   1.0
   (if (<= y -7.2e-65) x (if (<= y -1.3e-114) (- y) (if (<= y 1.0) x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.45e-6) {
		tmp = 1.0;
	} else if (y <= -7.2e-65) {
		tmp = x;
	} else if (y <= -1.3e-114) {
		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 <= (-1.45d-6)) then
        tmp = 1.0d0
    else if (y <= (-7.2d-65)) then
        tmp = x
    else if (y <= (-1.3d-114)) 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 <= -1.45e-6) {
		tmp = 1.0;
	} else if (y <= -7.2e-65) {
		tmp = x;
	} else if (y <= -1.3e-114) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.45e-6:
		tmp = 1.0
	elif y <= -7.2e-65:
		tmp = x
	elif y <= -1.3e-114:
		tmp = -y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.45e-6)
		tmp = 1.0;
	elseif (y <= -7.2e-65)
		tmp = x;
	elseif (y <= -1.3e-114)
		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 <= -1.45e-6)
		tmp = 1.0;
	elseif (y <= -7.2e-65)
		tmp = x;
	elseif (y <= -1.3e-114)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.45e-6], 1.0, If[LessEqual[y, -7.2e-65], x, If[LessEqual[y, -1.3e-114], (-y), If[LessEqual[y, 1.0], x, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4500000000000001e-6 or 1 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 72.0%

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

   if -1.4500000000000001e-6 < y < -7.1999999999999996e-65 or -1.30000000000000007e-114 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.4%

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

   if -7.1999999999999996e-65 < y < -1.30000000000000007e-114

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.9%

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

      1. neg-mul-1 73.9%

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

      2. distribute-neg-frac2 73.9%

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

      3. neg-sub0 73.9%

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

      4. associate--r- 73.9%

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

      5. metadata-eval 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in y around 0 73.9%

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

      1. neg-mul-1 73.9%

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

   8. Simplified 73.9%

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

Alternative 6: 86.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -750000000000 \lor \neg \left(y \leq 6800\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -750000000000.0) (not (<= y 6800.0)))
   (+ 1.0 (/ (- 1.0 x) y))
   (/ x (- 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -750000000000.0) || !(y <= 6800.0)) {
		tmp = 1.0 + ((1.0 - x) / y);
	} else {
		tmp = x / (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-750000000000.0d0)) .or. (.not. (y <= 6800.0d0))) then
        tmp = 1.0d0 + ((1.0d0 - x) / y)
    else
        tmp = x / (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -750000000000.0) || !(y <= 6800.0)) {
		tmp = 1.0 + ((1.0 - x) / y);
	} else {
		tmp = x / (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -750000000000.0) or not (y <= 6800.0):
		tmp = 1.0 + ((1.0 - x) / y)
	else:
		tmp = x / (1.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -750000000000.0) || !(y <= 6800.0))
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(x / Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -750000000000.0) || ~((y <= 6800.0)))
		tmp = 1.0 + ((1.0 - x) / y);
	else
		tmp = x / (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -750000000000.0], N[Not[LessEqual[y, 6800.0]], $MachinePrecision]], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5e11 or 6800 < y

   1. Initial program 99.9%

      \[\frac{x - y}{1 - y} \]
   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. sub-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 -7.5e11 < y < 6800

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 70.0%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -750000000000 \lor \neg \left(y \leq 6800\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.45e-6) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.45e-6) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.45d-6)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.45e-6) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.45e-6:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.45e-6)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.45e-6)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.45e-6], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4500000000000001e-6 or 1 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 72.0%

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

   if -1.4500000000000001e-6 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 69.5%

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

Alternative 8: 38.1% 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 39.9%

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

Reproduce

herbie shell --seed 2024108 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))