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

Percentage Accurate: 100.0% → 100.0%

Time: 5.3s

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. Add Preprocessing

Alternative 2: 98.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.85 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -0.85) (not (<= y 1.0))) (- 1.0 (/ x y)) (- x (* y (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -0.85) || !(y <= 1.0)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x - (y * (1.0 - 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 <= (-0.85d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x - (y * (1.0d0 - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -0.85) || !(y <= 1.0)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x - (y * (1.0 - x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -0.85) or not (y <= 1.0):
		tmp = 1.0 - (x / y)
	else:
		tmp = x - (y * (1.0 - x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -0.85) || !(y <= 1.0))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x - Float64(y * Float64(1.0 - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -0.85) || ~((y <= 1.0)))
		tmp = 1.0 - (x / y);
	else
		tmp = x - (y * (1.0 - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -0.85], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.849999999999999978 or 1 < y

   1. Initial program 100.0%

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

      1. expm1-log1p-u 48.5%

         \[\leadsto \frac{x - y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - y\right)\right)}} \]

   4. Applied egg-rr 48.5%

      \[\leadsto \frac{x - y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - y\right)\right)}} \]
   5. Step-by-step derivation

      1. expm1-undefine 48.5%

         \[\leadsto \frac{x - y}{\color{blue}{e^{\mathsf{log1p}\left(1 - y\right)} - 1}} \]

      2. sub-neg 48.5%

         \[\leadsto \frac{x - y}{\color{blue}{e^{\mathsf{log1p}\left(1 - y\right)} + \left(-1\right)}} \]

      3. log1p-undefine 48.5%

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

      4. rem-exp-log 100.0%

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

      5. associate-+r- 100.0%

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

      6. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\left(\color{blue}{2} - y\right) + \left(-1\right)} \]

      7. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\left(2 - y\right) + \color{blue}{-1}} \]

   6. Simplified 100.0%

      \[\leadsto \frac{x - y}{\color{blue}{\left(2 - y\right) + -1}} \]

   7. Taylor expanded in y around inf 98.3%

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

      1. neg-mul-1 98.3%

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

   9. Simplified 98.3%

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

   10. Taylor expanded in x around 0 98.3%

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

       1. neg-mul-1 98.3%

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

       2. unsub-neg 98.3%

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

   12. Simplified 98.3%

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

   if -0.849999999999999978 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. unsub-neg 98.9%

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

      3. mul-1-neg 98.9%

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

      4. sub-neg 98.9%

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

   5. Simplified 98.9%

      \[\leadsto \color{blue}{x - y \cdot \left(1 - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.85 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -450 \lor \neg \left(y \leq 28.5\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -450.0) (not (<= y 28.5))) (- 1.0 (/ x y)) (/ x (- 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -450.0) || !(y <= 28.5)) {
		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 <= (-450.0d0)) .or. (.not. (y <= 28.5d0))) 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 <= -450.0) || !(y <= 28.5)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -450.0) or not (y <= 28.5):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (1.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -450.0) || !(y <= 28.5))
		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 <= -450.0) || ~((y <= 28.5)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -450.0], N[Not[LessEqual[y, 28.5]], $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 < -450 or 28.5 < y

   1. Initial program 100.0%

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

      1. expm1-log1p-u 48.1%

         \[\leadsto \frac{x - y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - y\right)\right)}} \]

   4. Applied egg-rr 48.1%

      \[\leadsto \frac{x - y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - y\right)\right)}} \]
   5. Step-by-step derivation

      1. expm1-undefine 48.1%

         \[\leadsto \frac{x - y}{\color{blue}{e^{\mathsf{log1p}\left(1 - y\right)} - 1}} \]

      2. sub-neg 48.1%

         \[\leadsto \frac{x - y}{\color{blue}{e^{\mathsf{log1p}\left(1 - y\right)} + \left(-1\right)}} \]

      3. log1p-undefine 48.1%

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

      4. rem-exp-log 100.0%

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

      5. associate-+r- 100.0%

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

      6. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\left(\color{blue}{2} - y\right) + \left(-1\right)} \]

      7. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\left(2 - y\right) + \color{blue}{-1}} \]

   6. Simplified 100.0%

      \[\leadsto \frac{x - y}{\color{blue}{\left(2 - y\right) + -1}} \]

   7. Taylor expanded in y around inf 98.8%

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

      1. neg-mul-1 98.8%

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

   9. Simplified 98.8%

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

   10. Taylor expanded in x around 0 98.8%

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

       1. neg-mul-1 98.8%

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

       2. unsub-neg 98.8%

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

   12. Simplified 98.8%

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

   if -450 < y < 28.5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.6%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -450 \lor \neg \left(y \leq 28.5\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{-6} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6.9e-6) (not (<= y 1.0))) (- 1.0 (/ x y)) (+ x (* x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6.9e-6) || !(y <= 1.0)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x + (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 <= (-6.9d-6)) .or. (.not. (y <= 1.0d0))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -6.9e-6) || !(y <= 1.0)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x + (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6.9e-6) or not (y <= 1.0):
		tmp = 1.0 - (x / y)
	else:
		tmp = x + (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6.9e-6) || !(y <= 1.0))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -6.9e-6) || ~((y <= 1.0)))
		tmp = 1.0 - (x / y);
	else
		tmp = x + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6.9e-6], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9e-6 or 1 < y

   1. Initial program 100.0%

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

      1. expm1-log1p-u 48.9%

         \[\leadsto \frac{x - y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - y\right)\right)}} \]

   4. Applied egg-rr 48.9%

      \[\leadsto \frac{x - y}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - y\right)\right)}} \]
   5. Step-by-step derivation

      1. expm1-undefine 48.9%

         \[\leadsto \frac{x - y}{\color{blue}{e^{\mathsf{log1p}\left(1 - y\right)} - 1}} \]

      2. sub-neg 48.9%

         \[\leadsto \frac{x - y}{\color{blue}{e^{\mathsf{log1p}\left(1 - y\right)} + \left(-1\right)}} \]

      3. log1p-undefine 48.9%

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

      4. rem-exp-log 100.0%

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

      5. associate-+r- 100.0%

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

      6. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\left(\color{blue}{2} - y\right) + \left(-1\right)} \]

      7. metadata-eval 100.0%

         \[\leadsto \frac{x - y}{\left(2 - y\right) + \color{blue}{-1}} \]

   6. Simplified 100.0%

      \[\leadsto \frac{x - y}{\color{blue}{\left(2 - y\right) + -1}} \]

   7. Taylor expanded in y around inf 97.6%

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

      1. neg-mul-1 97.6%

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

   9. Simplified 97.6%

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

   10. Taylor expanded in x around 0 97.6%

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

       1. neg-mul-1 97.6%

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

       2. unsub-neg 97.6%

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

   12. Simplified 97.6%

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

   if -6.9e-6 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.0%

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

   4. Taylor expanded in y around 0 72.4%

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

      1. *-commutative 72.4%

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

   6. Simplified 72.4%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{-6} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.9e-6) 1.0 (if (<= y 1.0) (+ x (* x y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.9e-6) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x + (x * 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 <= (-6.9d-6)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x + (x * y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6.9e-6) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x + (x * y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.9e-6:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x + (x * y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.9e-6)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = Float64(x + Float64(x * y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6.9e-6)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x + (x * y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.9e-6], 1.0, If[LessEqual[y, 1.0], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9e-6 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 -6.9e-6 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.0%

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

   4. Taylor expanded in y around 0 72.4%

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

      1. *-commutative 72.4%

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

   6. Simplified 72.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.9e-6) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.9e-6) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-6.9d-6)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6.9e-6) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.9e-6:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.9e-6)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6.9e-6)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.9e-6], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9e-6 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 -6.9e-6 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.2%

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

Alternative 7: 39.4% 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 43.3%

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

Reproduce

herbie shell --seed 2024158 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))