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

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

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. Final simplification 100.0%

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

Alternative 2: 87.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -3800000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 3200:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (- 1.0 x) y))))
   (if (<= y -3800000.0)
     t_0
     (if (<= y -5.6e-43)
       (/ y (+ y -1.0))
       (if (<= y 3200.0) (/ x (- 1.0 y)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + ((1.0 - x) / y);
	double tmp;
	if (y <= -3800000.0) {
		tmp = t_0;
	} else if (y <= -5.6e-43) {
		tmp = y / (y + -1.0);
	} else if (y <= 3200.0) {
		tmp = x / (1.0 - y);
	} 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 + ((1.0d0 - x) / y)
    if (y <= (-3800000.0d0)) then
        tmp = t_0
    else if (y <= (-5.6d-43)) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 3200.0d0) then
        tmp = x / (1.0d0 - y)
    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 tmp;
	if (y <= -3800000.0) {
		tmp = t_0;
	} else if (y <= -5.6e-43) {
		tmp = y / (y + -1.0);
	} else if (y <= 3200.0) {
		tmp = x / (1.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + ((1.0 - x) / y)
	tmp = 0
	if y <= -3800000.0:
		tmp = t_0
	elif y <= -5.6e-43:
		tmp = y / (y + -1.0)
	elif y <= 3200.0:
		tmp = x / (1.0 - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(Float64(1.0 - x) / y))
	tmp = 0.0
	if (y <= -3800000.0)
		tmp = t_0;
	elseif (y <= -5.6e-43)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 3200.0)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + ((1.0 - x) / y);
	tmp = 0.0;
	if (y <= -3800000.0)
		tmp = t_0;
	elseif (y <= -5.6e-43)
		tmp = y / (y + -1.0);
	elseif (y <= 3200.0)
		tmp = x / (1.0 - y);
	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]}, If[LessEqual[y, -3800000.0], t$95$0, If[LessEqual[y, -5.6e-43], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3200.0], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8e6 or 3200 < y

   1. Initial program 99.9%

      \[\frac{x - y}{1 - y} \]

   2. Taylor expanded in y around inf 98.5%

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

      1. +-commutative 98.5%

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

      2. associate-+r+ 98.5%

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

      3. mul-1-neg 98.5%

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

      4. unsub-neg 98.5%

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

      5. div-sub 98.5%

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

      6. unsub-neg 98.5%

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

      7. mul-1-neg 98.5%

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

      8. +-commutative 98.5%

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

      9. metadata-eval 98.5%

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

      10. distribute-lft-in 98.5%

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

      11. metadata-eval 98.5%

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

      12. sub-neg 98.5%

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

      13. associate-*r/ 98.5%

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

      14. +-commutative 98.5%

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

      15. associate-*r/ 98.5%

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

      16. sub-neg 98.5%

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

      17. metadata-eval 98.5%

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

      18. distribute-lft-in 98.5%

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

      19. metadata-eval 98.5%

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

      20. +-commutative 98.5%

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

      21. mul-1-neg 98.5%

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

      22. unsub-neg 98.5%

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

   4. Simplified 98.5%

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

   if -3.8e6 < y < -5.5999999999999996e-43

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]

   2. Taylor expanded in x around 0 74.6%

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

      1. metadata-eval 74.6%

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

      2. times-frac 74.6%

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

      3. *-lft-identity 74.6%

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

      4. neg-mul-1 74.6%

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

      5. neg-sub0 74.6%

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

      6. associate--r- 74.6%

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

      7. metadata-eval 74.6%

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

   4. Simplified 74.6%

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

   if -5.5999999999999996e-43 < y < 3200

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]

   2. Taylor expanded in x around inf 80.0%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3800000:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 3200:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \end{array} \]

Alternative 3: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -10500000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 3000:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -10500000.0)
     t_0
     (if (<= y -3.5e-43)
       (/ y (+ y -1.0))
       (if (<= y 3000.0) (/ x (- 1.0 y)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -10500000.0) {
		tmp = t_0;
	} else if (y <= -3.5e-43) {
		tmp = y / (y + -1.0);
	} else if (y <= 3000.0) {
		tmp = x / (1.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    if (y <= (-10500000.0d0)) then
        tmp = t_0
    else if (y <= (-3.5d-43)) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 3000.0d0) then
        tmp = x / (1.0d0 - y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -10500000.0) {
		tmp = t_0;
	} else if (y <= -3.5e-43) {
		tmp = y / (y + -1.0);
	} else if (y <= 3000.0) {
		tmp = x / (1.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -10500000.0:
		tmp = t_0
	elif y <= -3.5e-43:
		tmp = y / (y + -1.0)
	elif y <= 3000.0:
		tmp = x / (1.0 - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -10500000.0)
		tmp = t_0;
	elseif (y <= -3.5e-43)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 3000.0)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -10500000.0)
		tmp = t_0;
	elseif (y <= -3.5e-43)
		tmp = y / (y + -1.0);
	elseif (y <= 3000.0)
		tmp = x / (1.0 - y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -10500000.0], t$95$0, If[LessEqual[y, -3.5e-43], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3000.0], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e7 or 3e3 < y

   1. Initial program 99.9%

      \[\frac{x - y}{1 - y} \]

   2. Taylor expanded in y around inf 98.5%

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

      1. +-commutative 98.5%

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

      2. associate-+r+ 98.5%

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

      3. mul-1-neg 98.5%

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

      4. unsub-neg 98.5%

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

      5. div-sub 98.5%

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

      6. unsub-neg 98.5%

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

      7. mul-1-neg 98.5%

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

      8. +-commutative 98.5%

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

      9. metadata-eval 98.5%

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

      10. distribute-lft-in 98.5%

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

      11. metadata-eval 98.5%

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

      12. sub-neg 98.5%

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

      13. associate-*r/ 98.5%

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

      14. +-commutative 98.5%

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

      15. associate-*r/ 98.5%

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

      16. sub-neg 98.5%

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

      17. metadata-eval 98.5%

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

      18. distribute-lft-in 98.5%

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

      19. metadata-eval 98.5%

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

      20. +-commutative 98.5%

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

      21. mul-1-neg 98.5%

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

      22. unsub-neg 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in x around inf 97.6%

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

      1. neg-mul-1 97.6%

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

      2. distribute-neg-frac 97.6%

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

   7. Simplified 97.6%

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

   if -1.05e7 < y < -3.49999999999999997e-43

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]

   2. Taylor expanded in x around 0 74.6%

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

      1. metadata-eval 74.6%

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

      2. times-frac 74.6%

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

      3. *-lft-identity 74.6%

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

      4. neg-mul-1 74.6%

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

      5. neg-sub0 74.6%

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

      6. associate--r- 74.6%

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

      7. metadata-eval 74.6%

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

   4. Simplified 74.6%

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

   if -3.49999999999999997e-43 < y < 3e3

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]

   2. Taylor expanded in x around inf 80.0%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -10500000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 3000:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 4: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+50}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.15e+50) 1.0 (if (<= y 6e+35) (/ x (- 1.0 y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.15e+50) {
		tmp = 1.0;
	} else if (y <= 6e+35) {
		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 <= (-2.15d+50)) then
        tmp = 1.0d0
    else if (y <= 6d+35) 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 <= -2.15e+50) {
		tmp = 1.0;
	} else if (y <= 6e+35) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.15e+50:
		tmp = 1.0
	elif y <= 6e+35:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.15e+50)
		tmp = 1.0;
	elseif (y <= 6e+35)
		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 <= -2.15e+50)
		tmp = 1.0;
	elseif (y <= 6e+35)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.15e+50], 1.0, If[LessEqual[y, 6e+35], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1499999999999999e50 or 5.99999999999999981e35 < y

   1. Initial program 99.9%

      \[\frac{x - y}{1 - y} \]

   2. Taylor expanded in y around inf 89.1%

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

   if -2.1499999999999999e50 < y < 5.99999999999999981e35

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]

   2. Taylor expanded in x around inf 74.5%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+50}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.5e-43) (/ y (+ y -1.0)) (if (<= y 6.6e+35) (/ x (- 1.0 y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.5e-43) {
		tmp = y / (y + -1.0);
	} else if (y <= 6.6e+35) {
		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 <= (-2.5d-43)) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 6.6d+35) 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 <= -2.5e-43) {
		tmp = y / (y + -1.0);
	} else if (y <= 6.6e+35) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.5e-43:
		tmp = y / (y + -1.0)
	elif y <= 6.6e+35:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.5e-43)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 6.6e+35)
		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 <= -2.5e-43)
		tmp = y / (y + -1.0);
	elseif (y <= 6.6e+35)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.5e-43], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+35], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000009e-43

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]

   2. Taylor expanded in x around 0 82.7%

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

      1. metadata-eval 82.7%

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

      2. times-frac 82.7%

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

      3. *-lft-identity 82.7%

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

      4. neg-mul-1 82.7%

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

      5. neg-sub0 82.7%

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

      6. associate--r- 82.7%

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

      7. metadata-eval 82.7%

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

   4. Simplified 82.7%

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

   if -2.50000000000000009e-43 < y < 6.6000000000000003e35

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]

   2. Taylor expanded in x around inf 78.2%

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

   if 6.6000000000000003e35 < y

   1. Initial program 99.8%

      \[\frac{x - y}{1 - y} \]

   2. Taylor expanded in y around inf 87.8%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 74.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.8e-26) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.8e-26) {
		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 <= (-5.8d-26)) 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 <= -5.8e-26) {
		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 <= -5.8e-26:
		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 <= -5.8e-26)
		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 <= -5.8e-26)
		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, -5.8e-26], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.7999999999999996e-26 or 1 < y

   1. Initial program 99.9%

      \[\frac{x - y}{1 - y} \]

   2. Taylor expanded in y around inf 78.8%

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

   if -5.7999999999999996e-26 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]

   2. Taylor expanded in y around 0 75.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 40.0% 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. Taylor expanded in y around inf 39.3%

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

3. Final simplification 39.3%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))