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

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 8

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, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. div-sub 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \frac{x}{1 - y} + \frac{y}{y + -1} \]
6. Add Preprocessing

Alternative 2: 86.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{1 - x}{y}\\ t_1 := \frac{y}{y + -1}\\ \mathbf{if}\;y \leq -15500:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.05:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (- 1.0 x) y))) (t_1 (/ y (+ y -1.0))))
   (if (<= y -15500.0)
     t_0
     (if (<= y -1.35e-62)
       t_1
       (if (<= y 2.55e-132)
         x
         (if (<= y 3.4e-105) t_1 (if (<= y 3.05) (/ x (- 1.0 y)) t_0)))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + ((1.0 - x) / y);
	double t_1 = y / (y + -1.0);
	double tmp;
	if (y <= -15500.0) {
		tmp = t_0;
	} else if (y <= -1.35e-62) {
		tmp = t_1;
	} else if (y <= 2.55e-132) {
		tmp = x;
	} else if (y <= 3.4e-105) {
		tmp = t_1;
	} else if (y <= 3.05) {
		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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + ((1.0d0 - x) / y)
    t_1 = y / (y + (-1.0d0))
    if (y <= (-15500.0d0)) then
        tmp = t_0
    else if (y <= (-1.35d-62)) then
        tmp = t_1
    else if (y <= 2.55d-132) then
        tmp = x
    else if (y <= 3.4d-105) then
        tmp = t_1
    else if (y <= 3.05d0) 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 t_1 = y / (y + -1.0);
	double tmp;
	if (y <= -15500.0) {
		tmp = t_0;
	} else if (y <= -1.35e-62) {
		tmp = t_1;
	} else if (y <= 2.55e-132) {
		tmp = x;
	} else if (y <= 3.4e-105) {
		tmp = t_1;
	} else if (y <= 3.05) {
		tmp = x / (1.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + ((1.0 - x) / y)
	t_1 = y / (y + -1.0)
	tmp = 0
	if y <= -15500.0:
		tmp = t_0
	elif y <= -1.35e-62:
		tmp = t_1
	elif y <= 2.55e-132:
		tmp = x
	elif y <= 3.4e-105:
		tmp = t_1
	elif y <= 3.05:
		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))
	t_1 = Float64(y / Float64(y + -1.0))
	tmp = 0.0
	if (y <= -15500.0)
		tmp = t_0;
	elseif (y <= -1.35e-62)
		tmp = t_1;
	elseif (y <= 2.55e-132)
		tmp = x;
	elseif (y <= 3.4e-105)
		tmp = t_1;
	elseif (y <= 3.05)
		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);
	t_1 = y / (y + -1.0);
	tmp = 0.0;
	if (y <= -15500.0)
		tmp = t_0;
	elseif (y <= -1.35e-62)
		tmp = t_1;
	elseif (y <= 2.55e-132)
		tmp = x;
	elseif (y <= 3.4e-105)
		tmp = t_1;
	elseif (y <= 3.05)
		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]}, Block[{t$95$1 = N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -15500.0], t$95$0, If[LessEqual[y, -1.35e-62], t$95$1, If[LessEqual[y, 2.55e-132], x, If[LessEqual[y, 3.4e-105], t$95$1, If[LessEqual[y, 3.05], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -15500 or 3.0499999999999998 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 98.7%

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

      1. +-commutative 98.7%

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

      2. mul-1-neg 98.7%

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

      3. sub-neg 98.7%

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

      4. div-sub 98.7%

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

   5. Simplified 98.7%

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

   if -15500 < y < -1.3500000000000001e-62 or 2.55000000000000003e-132 < y < 3.39999999999999992e-105

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.5%

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

      1. neg-mul-1 70.5%

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

      2. distribute-neg-frac2 70.5%

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

      3. neg-sub0 70.5%

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

      4. associate--r- 70.5%

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

      5. metadata-eval 70.5%

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

   5. Simplified 70.5%

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

   if -1.3500000000000001e-62 < y < 2.55000000000000003e-132

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.6%

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

   if 3.39999999999999992e-105 < y < 3.0499999999999998

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 69.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15500:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-62}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-105}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 3.05:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{y}{y + -1}\\ \mathbf{if}\;y \leq -29000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.05:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))) (t_1 (/ y (+ y -1.0))))
   (if (<= y -29000000.0)
     t_0
     (if (<= y -1.45e-62)
       t_1
       (if (<= y 2.55e-132)
         x
         (if (<= y 3.45e-105) t_1 (if (<= y 3.05) (/ x (- 1.0 y)) t_0)))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double t_1 = y / (y + -1.0);
	double tmp;
	if (y <= -29000000.0) {
		tmp = t_0;
	} else if (y <= -1.45e-62) {
		tmp = t_1;
	} else if (y <= 2.55e-132) {
		tmp = x;
	} else if (y <= 3.45e-105) {
		tmp = t_1;
	} else if (y <= 3.05) {
		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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    t_1 = y / (y + (-1.0d0))
    if (y <= (-29000000.0d0)) then
        tmp = t_0
    else if (y <= (-1.45d-62)) then
        tmp = t_1
    else if (y <= 2.55d-132) then
        tmp = x
    else if (y <= 3.45d-105) then
        tmp = t_1
    else if (y <= 3.05d0) 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 t_1 = y / (y + -1.0);
	double tmp;
	if (y <= -29000000.0) {
		tmp = t_0;
	} else if (y <= -1.45e-62) {
		tmp = t_1;
	} else if (y <= 2.55e-132) {
		tmp = x;
	} else if (y <= 3.45e-105) {
		tmp = t_1;
	} else if (y <= 3.05) {
		tmp = x / (1.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	t_1 = y / (y + -1.0)
	tmp = 0
	if y <= -29000000.0:
		tmp = t_0
	elif y <= -1.45e-62:
		tmp = t_1
	elif y <= 2.55e-132:
		tmp = x
	elif y <= 3.45e-105:
		tmp = t_1
	elif y <= 3.05:
		tmp = x / (1.0 - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	t_1 = Float64(y / Float64(y + -1.0))
	tmp = 0.0
	if (y <= -29000000.0)
		tmp = t_0;
	elseif (y <= -1.45e-62)
		tmp = t_1;
	elseif (y <= 2.55e-132)
		tmp = x;
	elseif (y <= 3.45e-105)
		tmp = t_1;
	elseif (y <= 3.05)
		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);
	t_1 = y / (y + -1.0);
	tmp = 0.0;
	if (y <= -29000000.0)
		tmp = t_0;
	elseif (y <= -1.45e-62)
		tmp = t_1;
	elseif (y <= 2.55e-132)
		tmp = x;
	elseif (y <= 3.45e-105)
		tmp = t_1;
	elseif (y <= 3.05)
		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]}, Block[{t$95$1 = N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -29000000.0], t$95$0, If[LessEqual[y, -1.45e-62], t$95$1, If[LessEqual[y, 2.55e-132], x, If[LessEqual[y, 3.45e-105], t$95$1, If[LessEqual[y, 3.05], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.9e7 or 3.0499999999999998 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 98.7%

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

      1. +-commutative 98.7%

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

      2. mul-1-neg 98.7%

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

      3. sub-neg 98.7%

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

      4. div-sub 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in x around inf 98.2%

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

      1. neg-mul-1 98.2%

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

      2. distribute-neg-frac2 98.2%

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

   8. Simplified 98.2%

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

   if -2.9e7 < y < -1.44999999999999993e-62 or 2.55000000000000003e-132 < y < 3.45000000000000014e-105

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.5%

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

      1. neg-mul-1 70.5%

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

      2. distribute-neg-frac2 70.5%

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

      3. neg-sub0 70.5%

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

      4. associate--r- 70.5%

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

      5. metadata-eval 70.5%

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

   5. Simplified 70.5%

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

   if -1.44999999999999993e-62 < y < 2.55000000000000003e-132

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.6%

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

   if 3.45000000000000014e-105 < y < 3.0499999999999998

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 69.6%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -29000000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-62}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{-105}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 3.05:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-62} \lor \neg \left(y \leq 2.55 \cdot 10^{-132} \lor \neg \left(y \leq 3.4 \cdot 10^{-105}\right) \land y \leq 5.2 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.4e-62)
         (not
          (or (<= y 2.55e-132) (and (not (<= y 3.4e-105)) (<= y 5.2e-49)))))
   (/ y (+ y -1.0))
   x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.4e-62) || !((y <= 2.55e-132) || (!(y <= 3.4e-105) && (y <= 5.2e-49)))) {
		tmp = y / (y + -1.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.4d-62)) .or. (.not. (y <= 2.55d-132) .or. (.not. (y <= 3.4d-105)) .and. (y <= 5.2d-49))) then
        tmp = y / (y + (-1.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.4e-62) || !((y <= 2.55e-132) || (!(y <= 3.4e-105) && (y <= 5.2e-49)))) {
		tmp = y / (y + -1.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.4e-62) or not ((y <= 2.55e-132) or (not (y <= 3.4e-105) and (y <= 5.2e-49))):
		tmp = y / (y + -1.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.4e-62) || !((y <= 2.55e-132) || (!(y <= 3.4e-105) && (y <= 5.2e-49))))
		tmp = Float64(y / Float64(y + -1.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.4e-62) || ~(((y <= 2.55e-132) || (~((y <= 3.4e-105)) && (y <= 5.2e-49)))))
		tmp = y / (y + -1.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.4e-62], N[Not[Or[LessEqual[y, 2.55e-132], And[N[Not[LessEqual[y, 3.4e-105]], $MachinePrecision], LessEqual[y, 5.2e-49]]]], $MachinePrecision]], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.40000000000000001e-62 or 2.55000000000000003e-132 < y < 3.39999999999999992e-105 or 5.1999999999999999e-49 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 72.0%

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

      1. neg-mul-1 72.0%

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

      2. distribute-neg-frac2 72.0%

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

      3. neg-sub0 72.0%

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

      4. associate--r- 72.0%

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

      5. metadata-eval 72.0%

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

   5. Simplified 72.0%

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

   if -1.40000000000000001e-62 < y < 2.55000000000000003e-132 or 3.39999999999999992e-105 < y < 5.1999999999999999e-49

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-62} \lor \neg \left(y \leq 2.55 \cdot 10^{-132} \lor \neg \left(y \leq 3.4 \cdot 10^{-105}\right) \land y \leq 5.2 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+23}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.4e+23) 1.0 (if (<= y 5.8e+23) (/ x (- 1.0 y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.4e+23) {
		tmp = 1.0;
	} else if (y <= 5.8e+23) {
		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 <= (-2.4d+23)) then
        tmp = 1.0d0
    else if (y <= 5.8d+23) 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 <= -2.4e+23) {
		tmp = 1.0;
	} else if (y <= 5.8e+23) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.4e+23:
		tmp = 1.0
	elif y <= 5.8e+23:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.4e+23)
		tmp = 1.0;
	elseif (y <= 5.8e+23)
		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 <= -2.4e+23)
		tmp = 1.0;
	elseif (y <= 5.8e+23)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.4e+23], 1.0, If[LessEqual[y, 5.8e+23], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e23 or 5.80000000000000025e23 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 75.7%

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

   if -2.4e23 < y < 5.80000000000000025e23

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.4%

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

Alternative 6: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -90000000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -90000000000000.0) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -90000000000000.0) {
		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 <= (-90000000000000.0d0)) 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 <= -90000000000000.0) {
		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 <= -90000000000000.0:
		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 <= -90000000000000.0)
		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 <= -90000000000000.0)
		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, -90000000000000.0], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -9e13 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.0%

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

   if -9e13 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.6%

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

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

   \[\leadsto \frac{y - x}{y + -1} \]
4. Add Preprocessing

Alternative 8: 39.0% 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. Add Preprocessing

3. Taylor expanded in y around inf 35.5%

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

Reproduce

herbie shell --seed 2024085 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))