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

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

Alternatives: 6

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: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -12600 \lor \neg \left(y \leq 55000\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -12600.0) (not (<= y 55000.0)))
   (+ 1.0 (/ (- 1.0 x) y))
   (/ x (- 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -12600.0) || !(y <= 55000.0)) {
		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 <= (-12600.0d0)) .or. (.not. (y <= 55000.0d0))) 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 <= -12600.0) || !(y <= 55000.0)) {
		tmp = 1.0 + ((1.0 - x) / y);
	} else {
		tmp = x / (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -12600.0) or not (y <= 55000.0):
		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 <= -12600.0) || !(y <= 55000.0))
		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 <= -12600.0) || ~((y <= 55000.0)))
		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, -12600.0], N[Not[LessEqual[y, 55000.0]], $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 < -12600 or 55000 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 98.9%

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

      1. +-commutative 98.9%

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

      2. associate-+r+ 98.9%

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

      3. mul-1-neg 98.9%

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

      4. unsub-neg 98.9%

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

      5. div-sub 98.9%

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

      6. unsub-neg 98.9%

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

      7. mul-1-neg 98.9%

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

      8. +-commutative 98.9%

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

      9. metadata-eval 98.9%

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

      10. distribute-lft-in 98.9%

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

      11. metadata-eval 98.9%

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

      12. sub-neg 98.9%

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

      13. associate-*r/ 98.9%

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

      14. +-commutative 98.9%

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

      15. associate-*r/ 98.9%

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

      16. sub-neg 98.9%

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

      17. metadata-eval 98.9%

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

      18. distribute-lft-in 98.9%

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

      19. metadata-eval 98.9%

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

      20. +-commutative 98.9%

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

      21. mul-1-neg 98.9%

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

      22. unsub-neg 98.9%

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

   4. Simplified 98.9%

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

   if -12600 < y < 55000

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.3%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12600 \lor \neg \left(y \leq 55000\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]

Alternative 3: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-7} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.5e-7) (not (<= y 1.0))) (- 1.0 (/ x y)) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.5e-7) || !(y <= 1.0)) {
		tmp = 1.0 - (x / y);
	} 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 <= (-2.5d-7)) .or. (.not. (y <= 1.0d0))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.5e-7) || !(y <= 1.0)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.5e-7) or not (y <= 1.0):
		tmp = 1.0 - (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.5e-7) || !(y <= 1.0))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.5e-7) || ~((y <= 1.0)))
		tmp = 1.0 - (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.5e-7], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999989e-7 or 1 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 96.2%

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

      1. +-commutative 96.2%

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

      2. associate-+r+ 96.2%

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

      3. mul-1-neg 96.2%

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

      4. unsub-neg 96.2%

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

      5. div-sub 96.2%

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

      6. unsub-neg 96.2%

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

      7. mul-1-neg 96.2%

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

      8. +-commutative 96.2%

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

      9. metadata-eval 96.2%

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

      10. distribute-lft-in 96.2%

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

      11. metadata-eval 96.2%

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

      12. sub-neg 96.2%

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

      13. associate-*r/ 96.2%

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

      14. +-commutative 96.2%

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

      15. associate-*r/ 96.2%

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

      16. sub-neg 96.2%

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

      17. metadata-eval 96.2%

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

      18. distribute-lft-in 96.2%

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

      19. metadata-eval 96.2%

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

      20. +-commutative 96.2%

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

      21. mul-1-neg 96.2%

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

      22. unsub-neg 96.2%

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

   4. Simplified 96.2%

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

   5. Taylor expanded in x around inf 95.6%

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

      1. neg-mul-1 95.6%

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

      2. distribute-neg-frac 95.6%

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

   7. Simplified 95.6%

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

   8. Taylor expanded in x around 0 95.6%

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

      1. mul-1-neg 95.6%

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

      2. sub-neg 95.6%

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

   10. Simplified 95.6%

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

   if -2.49999999999999989e-7 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.5%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-7} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -280000000 \lor \neg \left(y \leq 140000\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -280000000.0) (not (<= y 140000.0)))
   (- 1.0 (/ x y))
   (/ x (- 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -280000000.0) || !(y <= 140000.0)) {
		tmp = 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 <= (-280000000.0d0)) .or. (.not. (y <= 140000.0d0))) then
        tmp = 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 <= -280000000.0) || !(y <= 140000.0)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -280000000.0) or not (y <= 140000.0):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (1.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -280000000.0) || !(y <= 140000.0))
		tmp = Float64(1.0 - Float64(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 <= -280000000.0) || ~((y <= 140000.0)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -280000000.0], N[Not[LessEqual[y, 140000.0]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e8 or 1.4e5 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r+ 99.8%

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

      3. mul-1-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. div-sub 99.8%

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

      6. unsub-neg 99.8%

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

      7. mul-1-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. metadata-eval 99.8%

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

      10. distribute-lft-in 99.8%

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

      11. metadata-eval 99.8%

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

      12. sub-neg 99.8%

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

      13. associate-*r/ 99.8%

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

      14. +-commutative 99.8%

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

      15. associate-*r/ 99.8%

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

      16. sub-neg 99.8%

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

      17. metadata-eval 99.8%

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

      18. distribute-lft-in 99.8%

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

      19. metadata-eval 99.8%

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

      20. +-commutative 99.8%

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

      21. mul-1-neg 99.8%

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

      22. unsub-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in x around inf 99.5%

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

      1. neg-mul-1 99.5%

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

      2. distribute-neg-frac 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in x around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. sub-neg 99.5%

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

   10. Simplified 99.5%

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

   if -2.8e8 < y < 1.4e5

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.4%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -280000000 \lor \neg \left(y \leq 140000\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]

Alternative 5: 73.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2150:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2150.0) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2150.0) {
		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 <= (-2150.0d0)) 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 <= -2150.0) {
		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 <= -2150.0:
		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 <= -2150.0)
		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 <= -2150.0)
		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, -2150.0], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2150 or 1 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 72.9%

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

   if -2150 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.9%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2150:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 39.3% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around inf 44.3%

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

3. Final simplification 44.3%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))