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

Percentage Accurate: 100.0% → 100.0%

Time: 4.4s

Alternatives: 7

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: 86.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{1 - x}{y}\\ t_1 := \frac{x}{1 - y}\\ \mathbf{if}\;y \leq -740:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 13500:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (- 1.0 x) y))) (t_1 (/ x (- 1.0 y))))
   (if (<= y -740.0)
     t_0
     (if (<= y 6.2e-30)
       t_1
       (if (<= y 2e-15) (/ y (+ y -1.0)) (if (<= y 13500.0) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + ((1.0 - x) / y);
	double t_1 = x / (1.0 - y);
	double tmp;
	if (y <= -740.0) {
		tmp = t_0;
	} else if (y <= 6.2e-30) {
		tmp = t_1;
	} else if (y <= 2e-15) {
		tmp = y / (y + -1.0);
	} else if (y <= 13500.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + ((1.0d0 - x) / y)
    t_1 = x / (1.0d0 - y)
    if (y <= (-740.0d0)) then
        tmp = t_0
    else if (y <= 6.2d-30) then
        tmp = t_1
    else if (y <= 2d-15) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 13500.0d0) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + ((1.0 - x) / y);
	double t_1 = x / (1.0 - y);
	double tmp;
	if (y <= -740.0) {
		tmp = t_0;
	} else if (y <= 6.2e-30) {
		tmp = t_1;
	} else if (y <= 2e-15) {
		tmp = y / (y + -1.0);
	} else if (y <= 13500.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + ((1.0 - x) / y)
	t_1 = x / (1.0 - y)
	tmp = 0
	if y <= -740.0:
		tmp = t_0
	elif y <= 6.2e-30:
		tmp = t_1
	elif y <= 2e-15:
		tmp = y / (y + -1.0)
	elif y <= 13500.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(Float64(1.0 - x) / y))
	t_1 = Float64(x / Float64(1.0 - y))
	tmp = 0.0
	if (y <= -740.0)
		tmp = t_0;
	elseif (y <= 6.2e-30)
		tmp = t_1;
	elseif (y <= 2e-15)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 13500.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + ((1.0 - x) / y);
	t_1 = x / (1.0 - y);
	tmp = 0.0;
	if (y <= -740.0)
		tmp = t_0;
	elseif (y <= 6.2e-30)
		tmp = t_1;
	elseif (y <= 2e-15)
		tmp = y / (y + -1.0);
	elseif (y <= 13500.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -740.0], t$95$0, If[LessEqual[y, 6.2e-30], t$95$1, If[LessEqual[y, 2e-15], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 13500.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -740 or 13500 < 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 -740 < y < 6.19999999999999982e-30 or 2.0000000000000002e-15 < y < 13500

   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 6.19999999999999982e-30 < y < 2.0000000000000002e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. metadata-eval 100.0%

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

      2. times-frac 100.0%

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

      3. *-lft-identity 100.0%

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

      4. neg-mul-1 100.0%

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

      5. neg-sub0 100.0%

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

      6. associate--r- 100.0%

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

      7. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -740:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 13500:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x}{1 - y}\\ \mathbf{if}\;y \leq -740:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 300000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))) (t_1 (/ x (- 1.0 y))))
   (if (<= y -740.0)
     t_0
     (if (<= y 2.3e-29)
       t_1
       (if (<= y 3.05e-15)
         (/ y (+ y -1.0))
         (if (<= y 300000000.0) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double t_1 = x / (1.0 - y);
	double tmp;
	if (y <= -740.0) {
		tmp = t_0;
	} else if (y <= 2.3e-29) {
		tmp = t_1;
	} else if (y <= 3.05e-15) {
		tmp = y / (y + -1.0);
	} else if (y <= 300000000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    t_1 = x / (1.0d0 - y)
    if (y <= (-740.0d0)) then
        tmp = t_0
    else if (y <= 2.3d-29) then
        tmp = t_1
    else if (y <= 3.05d-15) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 300000000.0d0) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double t_1 = x / (1.0 - y);
	double tmp;
	if (y <= -740.0) {
		tmp = t_0;
	} else if (y <= 2.3e-29) {
		tmp = t_1;
	} else if (y <= 3.05e-15) {
		tmp = y / (y + -1.0);
	} else if (y <= 300000000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	t_1 = x / (1.0 - y)
	tmp = 0
	if y <= -740.0:
		tmp = t_0
	elif y <= 2.3e-29:
		tmp = t_1
	elif y <= 3.05e-15:
		tmp = y / (y + -1.0)
	elif y <= 300000000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	t_1 = Float64(x / Float64(1.0 - y))
	tmp = 0.0
	if (y <= -740.0)
		tmp = t_0;
	elseif (y <= 2.3e-29)
		tmp = t_1;
	elseif (y <= 3.05e-15)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 300000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x / y);
	t_1 = x / (1.0 - y);
	tmp = 0.0;
	if (y <= -740.0)
		tmp = t_0;
	elseif (y <= 2.3e-29)
		tmp = t_1;
	elseif (y <= 3.05e-15)
		tmp = y / (y + -1.0);
	elseif (y <= 300000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -740.0], t$95$0, If[LessEqual[y, 2.3e-29], t$95$1, If[LessEqual[y, 3.05e-15], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 300000000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -740 or 3e8 < 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%

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

   6. Taylor expanded in x around inf 98.4%

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

      1. neg-mul-1 98.4%

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

      2. distribute-neg-frac 98.4%

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

   8. Simplified 98.4%

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

   if -740 < y < 2.29999999999999991e-29 or 3.04999999999999986e-15 < y < 3e8

   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 2.29999999999999991e-29 < y < 3.04999999999999986e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. metadata-eval 100.0%

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

      2. times-frac 100.0%

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

      3. *-lft-identity 100.0%

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

      4. neg-mul-1 100.0%

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

      5. neg-sub0 100.0%

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

      6. associate--r- 100.0%

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

      7. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -740:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 300000000:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-28} \lor \neg \left(y \leq 9 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.2e-28) (not (<= y 9e-29))) (/ y (+ y -1.0)) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.2e-28) || !(y <= 9e-29)) {
		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 <= (-4.2d-28)) .or. (.not. (y <= 9d-29))) 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 <= -4.2e-28) || !(y <= 9e-29)) {
		tmp = y / (y + -1.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.2e-28) or not (y <= 9e-29):
		tmp = y / (y + -1.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.2e-28) || !(y <= 9e-29))
		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 <= -4.2e-28) || ~((y <= 9e-29)))
		tmp = y / (y + -1.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.2e-28], N[Not[LessEqual[y, 9e-29]], $MachinePrecision]], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.20000000000000013e-28 or 8.9999999999999996e-29 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.3%

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

      1. metadata-eval 79.3%

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

      2. times-frac 79.3%

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

      3. *-lft-identity 79.3%

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

      4. neg-mul-1 79.3%

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

      5. neg-sub0 79.3%

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

      6. associate--r- 79.3%

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

      7. metadata-eval 79.3%

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

   5. Simplified 79.3%

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

   if -4.20000000000000013e-28 < y < 8.9999999999999996e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.1%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-28} \lor \neg \left(y \leq 9 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -740:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -740.0) 1.0 (if (<= y 9.2e+26) (/ x (- 1.0 y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -740.0) {
		tmp = 1.0;
	} else if (y <= 9.2e+26) {
		tmp = x / (1.0 - 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 <= (-740.0d0)) then
        tmp = 1.0d0
    else if (y <= 9.2d+26) then
        tmp = x / (1.0d0 - y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -740.0) {
		tmp = 1.0;
	} else if (y <= 9.2e+26) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -740.0:
		tmp = 1.0
	elif y <= 9.2e+26:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -740.0)
		tmp = 1.0;
	elseif (y <= 9.2e+26)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -740.0)
		tmp = 1.0;
	elseif (y <= 9.2e+26)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -740.0], 1.0, If[LessEqual[y, 9.2e+26], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -740 or 9.2000000000000002e26 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.5%

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

   if -740 < y < 9.2000000000000002e26

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.9%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -740:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -600:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -600.0) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -600.0) {
		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 <= (-600.0d0)) 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 <= -600.0) {
		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 <= -600.0:
		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 <= -600.0)
		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 <= -600.0)
		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, -600.0], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -600 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.0%

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

   if -600 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.3%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -600:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.6% 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 39.1%

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

4. Final simplification 39.1%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024018 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))