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

Percentage Accurate: 100.0% → 100.0%

Time: 15.8s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 87.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6000:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6000.0)
   (+ 1.0 (/ (- 1.0 x) y))
   (if (<= y -2.95e-31)
     (/ y (+ y -1.0))
     (if (<= y 6.6e+15) (/ x (- 1.0 y)) (- 1.0 (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6000.0) {
		tmp = 1.0 + ((1.0 - x) / y);
	} else if (y <= -2.95e-31) {
		tmp = y / (y + -1.0);
	} else if (y <= 6.6e+15) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-6000.0d0)) then
        tmp = 1.0d0 + ((1.0d0 - x) / y)
    else if (y <= (-2.95d-31)) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 6.6d+15) then
        tmp = x / (1.0d0 - y)
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6000.0) {
		tmp = 1.0 + ((1.0 - x) / y);
	} else if (y <= -2.95e-31) {
		tmp = y / (y + -1.0);
	} else if (y <= 6.6e+15) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6000.0:
		tmp = 1.0 + ((1.0 - x) / y)
	elif y <= -2.95e-31:
		tmp = y / (y + -1.0)
	elif y <= 6.6e+15:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6000.0)
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) / y));
	elseif (y <= -2.95e-31)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 6.6e+15)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6000.0)
		tmp = 1.0 + ((1.0 - x) / y);
	elseif (y <= -2.95e-31)
		tmp = y / (y + -1.0);
	elseif (y <= 6.6e+15)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6000.0], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.95e-31], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+15], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6e3

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 97.1%

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

      1. +-commutative 97.1%

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

      2. mul-1-neg 97.1%

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

      3. sub-neg 97.1%

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

      4. div-sub 97.1%

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

   5. Simplified 97.1%

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

   if -6e3 < y < -2.95000000000000016e-31

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 90.3%

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

      1. neg-mul-1 90.3%

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

      2. distribute-neg-frac2 90.3%

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

      3. neg-sub0 90.3%

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

      4. associate--r- 90.3%

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

      5. metadata-eval 90.3%

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

   5. Simplified 90.3%

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

   if -2.95000000000000016e-31 < y < 6.6e15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.3%

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

   if 6.6e15 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.1%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}}{1 - y} \]

      2. pow3 98.2%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x - y}\right)}^{3}}}{1 - y} \]

   4. Applied egg-rr 98.2%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x - y}\right)}^{3}}}{1 - y} \]

   5. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. div-sub 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. neg-mul-1 100.0%

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

      8. metadata-eval 100.0%

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

      9. distribute-lft-in 100.0%

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

      10. metadata-eval 100.0%

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

      11. sub-neg 100.0%

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

      12. associate-*r/ 100.0%

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

      13. mul-1-neg 100.0%

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

      14. unsub-neg 100.0%

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

      15. sub-neg 100.0%

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

      16. remove-double-neg 100.0%

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

      17. distribute-neg-in 100.0%

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

      18. +-commutative 100.0%

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

      19. neg-mul-1 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 100.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6000:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -14500:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -14500.0)
     t_0
     (if (<= y -9e-36)
       (/ y (+ y -1.0))
       (if (<= y 6.6e+15) (/ x (- 1.0 y)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -14500.0) {
		tmp = t_0;
	} else if (y <= -9e-36) {
		tmp = y / (y + -1.0);
	} else if (y <= 6.6e+15) {
		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 <= (-14500.0d0)) then
        tmp = t_0
    else if (y <= (-9d-36)) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 6.6d+15) 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 <= -14500.0) {
		tmp = t_0;
	} else if (y <= -9e-36) {
		tmp = y / (y + -1.0);
	} else if (y <= 6.6e+15) {
		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 <= -14500.0:
		tmp = t_0
	elif y <= -9e-36:
		tmp = y / (y + -1.0)
	elif y <= 6.6e+15:
		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 <= -14500.0)
		tmp = t_0;
	elseif (y <= -9e-36)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 6.6e+15)
		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 <= -14500.0)
		tmp = t_0;
	elseif (y <= -9e-36)
		tmp = y / (y + -1.0);
	elseif (y <= 6.6e+15)
		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, -14500.0], t$95$0, If[LessEqual[y, -9e-36], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+15], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -14500 or 6.6e15 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.1%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}}{1 - y} \]

      2. pow3 98.1%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x - y}\right)}^{3}}}{1 - y} \]

   4. Applied egg-rr 98.1%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x - y}\right)}^{3}}}{1 - y} \]

   5. Taylor expanded in y around inf 98.8%

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

      1. +-commutative 98.8%

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

      2. mul-1-neg 98.8%

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

      3. sub-neg 98.8%

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

      4. div-sub 98.8%

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

      5. sub-neg 98.8%

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

      6. +-commutative 98.8%

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

      7. neg-mul-1 98.8%

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

      8. metadata-eval 98.8%

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

      9. distribute-lft-in 98.8%

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

      10. metadata-eval 98.8%

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

      11. sub-neg 98.8%

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

      12. associate-*r/ 98.8%

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

      13. mul-1-neg 98.8%

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

      14. unsub-neg 98.8%

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

      15. sub-neg 98.8%

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

      16. remove-double-neg 98.8%

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

      17. distribute-neg-in 98.8%

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

      18. +-commutative 98.8%

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

      19. neg-mul-1 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in x around inf 98.8%

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

   if -14500 < y < -9.00000000000000047e-36

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 90.3%

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

      1. neg-mul-1 90.3%

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

      2. distribute-neg-frac2 90.3%

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

      3. neg-sub0 90.3%

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

      4. associate--r- 90.3%

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

      5. metadata-eval 90.3%

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

   5. Simplified 90.3%

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

   if -9.00000000000000047e-36 < y < 6.6e15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.3%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -14500:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -0.215:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -0.215)
     t_0
     (if (<= y -5.5e-30)
       (* y (- -1.0 y))
       (if (<= y 6.6e+15) (/ x (- 1.0 y)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -0.215) {
		tmp = t_0;
	} else if (y <= -5.5e-30) {
		tmp = y * (-1.0 - y);
	} else if (y <= 6.6e+15) {
		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 <= (-0.215d0)) then
        tmp = t_0
    else if (y <= (-5.5d-30)) then
        tmp = y * ((-1.0d0) - y)
    else if (y <= 6.6d+15) 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 <= -0.215) {
		tmp = t_0;
	} else if (y <= -5.5e-30) {
		tmp = y * (-1.0 - y);
	} else if (y <= 6.6e+15) {
		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 <= -0.215:
		tmp = t_0
	elif y <= -5.5e-30:
		tmp = y * (-1.0 - y)
	elif y <= 6.6e+15:
		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 <= -0.215)
		tmp = t_0;
	elseif (y <= -5.5e-30)
		tmp = Float64(y * Float64(-1.0 - y));
	elseif (y <= 6.6e+15)
		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 <= -0.215)
		tmp = t_0;
	elseif (y <= -5.5e-30)
		tmp = y * (-1.0 - y);
	elseif (y <= 6.6e+15)
		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, -0.215], t$95$0, If[LessEqual[y, -5.5e-30], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+15], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.214999999999999997 or 6.6e15 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.1%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}}{1 - y} \]

      2. pow3 98.1%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x - y}\right)}^{3}}}{1 - y} \]

   4. Applied egg-rr 98.1%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x - y}\right)}^{3}}}{1 - y} \]

   5. Taylor expanded in y around inf 98.8%

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

      1. +-commutative 98.8%

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

      2. mul-1-neg 98.8%

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

      3. sub-neg 98.8%

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

      4. div-sub 98.8%

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

      5. sub-neg 98.8%

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

      6. +-commutative 98.8%

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

      7. neg-mul-1 98.8%

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

      8. metadata-eval 98.8%

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

      9. distribute-lft-in 98.8%

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

      10. metadata-eval 98.8%

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

      11. sub-neg 98.8%

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

      12. associate-*r/ 98.8%

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

      13. mul-1-neg 98.8%

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

      14. unsub-neg 98.8%

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

      15. sub-neg 98.8%

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

      16. remove-double-neg 98.8%

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

      17. distribute-neg-in 98.8%

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

      18. +-commutative 98.8%

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

      19. neg-mul-1 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in x around inf 98.8%

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

   if -0.214999999999999997 < y < -5.49999999999999976e-30

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 90.3%

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

      1. neg-mul-1 90.3%

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

      2. distribute-neg-frac2 90.3%

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

      3. neg-sub0 90.3%

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

      4. associate--r- 90.3%

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

      5. metadata-eval 90.3%

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

   5. Simplified 90.3%

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

   6. Taylor expanded in y around 0 84.3%

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

      1. sub-neg 84.3%

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

      2. neg-mul-1 84.3%

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

      3. metadata-eval 84.3%

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

      4. +-commutative 84.3%

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

      5. sub-neg 84.3%

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

   8. Simplified 84.3%

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

   if -5.49999999999999976e-30 < y < 6.6e15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.3%

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

Alternative 5: 86.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -0.26:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -0.26)
     t_0
     (if (<= y -4.2e-40) (* y (- -1.0 y)) (if (<= y 1.0) x t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -0.26) {
		tmp = t_0;
	} else if (y <= -4.2e-40) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.0) {
		tmp = x;
	} 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 <= (-0.26d0)) then
        tmp = t_0
    else if (y <= (-4.2d-40)) then
        tmp = y * ((-1.0d0) - y)
    else if (y <= 1.0d0) then
        tmp = x
    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 <= -0.26) {
		tmp = t_0;
	} else if (y <= -4.2e-40) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -0.26:
		tmp = t_0
	elif y <= -4.2e-40:
		tmp = y * (-1.0 - y)
	elif y <= 1.0:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -0.26)
		tmp = t_0;
	elseif (y <= -4.2e-40)
		tmp = Float64(y * Float64(-1.0 - y));
	elseif (y <= 1.0)
		tmp = x;
	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 <= -0.26)
		tmp = t_0;
	elseif (y <= -4.2e-40)
		tmp = y * (-1.0 - y);
	elseif (y <= 1.0)
		tmp = x;
	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, -0.26], t$95$0, If[LessEqual[y, -4.2e-40], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], x, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.26000000000000001 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 98.1%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}}{1 - y} \]

      2. pow3 98.1%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x - y}\right)}^{3}}}{1 - y} \]

   4. Applied egg-rr 98.1%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x - y}\right)}^{3}}}{1 - y} \]

   5. Taylor expanded in y around inf 98.3%

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

      1. +-commutative 98.3%

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

      2. mul-1-neg 98.3%

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

      3. sub-neg 98.3%

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

      4. div-sub 98.3%

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

      5. sub-neg 98.3%

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

      6. +-commutative 98.3%

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

      7. neg-mul-1 98.3%

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

      8. metadata-eval 98.3%

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

      9. distribute-lft-in 98.3%

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

      10. metadata-eval 98.3%

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

      11. sub-neg 98.3%

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

      12. associate-*r/ 98.3%

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

      13. mul-1-neg 98.3%

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

      14. unsub-neg 98.3%

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

      15. sub-neg 98.3%

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

      16. remove-double-neg 98.3%

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

      17. distribute-neg-in 98.3%

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

      18. +-commutative 98.3%

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

      19. neg-mul-1 98.3%

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

   7. Simplified 98.3%

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

   8. Taylor expanded in x around inf 98.3%

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

   if -0.26000000000000001 < y < -4.20000000000000036e-40

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 90.3%

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

      1. neg-mul-1 90.3%

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

      2. distribute-neg-frac2 90.3%

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

      3. neg-sub0 90.3%

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

      4. associate--r- 90.3%

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

      5. metadata-eval 90.3%

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

   5. Simplified 90.3%

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

   6. Taylor expanded in y around 0 84.3%

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

      1. sub-neg 84.3%

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

      2. neg-mul-1 84.3%

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

      3. metadata-eval 84.3%

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

      4. +-commutative 84.3%

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

      5. sub-neg 84.3%

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

   8. Simplified 84.3%

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

   if -4.20000000000000036e-40 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 71.8%

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

Alternative 6: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -49000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -49000.0)
   1.0
   (if (<= y -4.6e-31) (* y (- -1.0 y)) (if (<= y 1.0) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -49000.0) {
		tmp = 1.0;
	} else if (y <= -4.6e-31) {
		tmp = y * (-1.0 - 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 <= (-49000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-4.6d-31)) then
        tmp = y * ((-1.0d0) - 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 <= -49000.0) {
		tmp = 1.0;
	} else if (y <= -4.6e-31) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -49000.0:
		tmp = 1.0
	elif y <= -4.6e-31:
		tmp = y * (-1.0 - y)
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -49000.0)
		tmp = 1.0;
	elseif (y <= -4.6e-31)
		tmp = Float64(y * Float64(-1.0 - 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 <= -49000.0)
		tmp = 1.0;
	elseif (y <= -4.6e-31)
		tmp = y * (-1.0 - y);
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -49000.0], 1.0, If[LessEqual[y, -4.6e-31], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -49000 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.2%

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

   if -49000 < y < -4.5999999999999997e-31

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 81.4%

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

      1. neg-mul-1 81.4%

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

      2. distribute-neg-frac2 81.4%

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

      3. neg-sub0 81.4%

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

      4. associate--r- 81.4%

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

      5. metadata-eval 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in y around 0 76.9%

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

      1. sub-neg 76.9%

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

      2. neg-mul-1 76.9%

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

      3. metadata-eval 76.9%

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

      4. +-commutative 76.9%

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

      5. sub-neg 76.9%

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

   8. Simplified 76.9%

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

   if -4.5999999999999997e-31 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 71.8%

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

Alternative 7: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -28500000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-39}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -28500000.0) 1.0 (if (<= y -2.5e-39) (- y) (if (<= y 1.0) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -28500000.0) {
		tmp = 1.0;
	} else if (y <= -2.5e-39) {
		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 <= (-28500000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-2.5d-39)) 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 <= -28500000.0) {
		tmp = 1.0;
	} else if (y <= -2.5e-39) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -28500000.0:
		tmp = 1.0
	elif y <= -2.5e-39:
		tmp = -y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -28500000.0)
		tmp = 1.0;
	elseif (y <= -2.5e-39)
		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 <= -28500000.0)
		tmp = 1.0;
	elseif (y <= -2.5e-39)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -28500000.0], 1.0, If[LessEqual[y, -2.5e-39], (-y), If[LessEqual[y, 1.0], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.85e7 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 74.3%

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

   if -2.85e7 < y < -2.4999999999999999e-39

   1. Initial program 99.9%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 97.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}}{1 - y} \]

      2. pow3 97.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x - y}\right)}^{3}}}{1 - y} \]

   4. Applied egg-rr 97.4%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x - y}\right)}^{3}}}{1 - y} \]

   5. Taylor expanded in y around -inf 67.8%

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

      1. neg-mul-1 67.8%

         \[\leadsto \frac{{\color{blue}{\left(-\sqrt[3]{y}\right)}}^{3}}{1 - y} \]

   7. Simplified 67.8%

      \[\leadsto \frac{{\color{blue}{\left(-\sqrt[3]{y}\right)}}^{3}}{1 - y} \]

   8. Taylor expanded in y around 0 59.3%

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

      1. neg-mul-1 59.3%

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

   10. Simplified 59.3%

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

   if -2.4999999999999999e-39 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 71.8%

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

Alternative 8: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.75e-21) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.75e-21) {
		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 <= (-2.75d-21)) 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 <= -2.75e-21) {
		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 <= -2.75e-21:
		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 <= -2.75e-21)
		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 <= -2.75e-21)
		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, -2.75e-21], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.74999999999999989e-21 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 70.3%

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

   if -2.74999999999999989e-21 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 69.9%

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

Alternative 9: 38.5% 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 37.6%

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

Reproduce

herbie shell --seed 2024143 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))