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

Percentage Accurate: 100.0% → 100.0%

Time: 4.2s

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: 87.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1300 \lor \neg \left(y \leq 7.8\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1300.0) (not (<= y 7.8)))
   (+ 1.0 (/ (- 1.0 x) y))
   (* x (/ 1.0 (- 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1300.0) || !(y <= 7.8)) {
		tmp = 1.0 + ((1.0 - x) / y);
	} else {
		tmp = x * (1.0 / (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 <= (-1300.0d0)) .or. (.not. (y <= 7.8d0))) then
        tmp = 1.0d0 + ((1.0d0 - x) / y)
    else
        tmp = x * (1.0d0 / (1.0d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1300.0) || !(y <= 7.8)) {
		tmp = 1.0 + ((1.0 - x) / y);
	} else {
		tmp = x * (1.0 / (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1300.0) or not (y <= 7.8):
		tmp = 1.0 + ((1.0 - x) / y)
	else:
		tmp = x * (1.0 / (1.0 - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1300.0) || !(y <= 7.8))
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(x * Float64(1.0 / Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1300.0) || ~((y <= 7.8)))
		tmp = 1.0 + ((1.0 - x) / y);
	else
		tmp = x * (1.0 / (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1300.0], N[Not[LessEqual[y, 7.8]], $MachinePrecision]], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1300 or 7.79999999999999982 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 98.9%

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

      1. +-commutative 98.9%

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

      2. mul-1-neg 98.9%

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

      3. unsub-neg 98.9%

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

      4. div-sub 98.9%

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

   4. Simplified 98.9%

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

   if -1300 < y < 7.79999999999999982

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.6%

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

      1. clear-num 80.5%

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

      2. associate-/r/ 80.6%

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

   4. Applied egg-rr 80.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1300 \lor \neg \left(y \leq 7.8\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{1 - y}\\ \end{array} \]

Alternative 3: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+48}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.1e+48) 1.0 (if (<= y 7e+16) (/ x (- 1.0 y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.1e+48) {
		tmp = 1.0;
	} else if (y <= 7e+16) {
		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 <= (-2.1d+48)) then
        tmp = 1.0d0
    else if (y <= 7d+16) 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 <= -2.1e+48) {
		tmp = 1.0;
	} else if (y <= 7e+16) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.1e+48:
		tmp = 1.0
	elif y <= 7e+16:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.1e+48)
		tmp = 1.0;
	elseif (y <= 7e+16)
		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 <= -2.1e+48)
		tmp = 1.0;
	elseif (y <= 7e+16)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.1e+48], 1.0, If[LessEqual[y, 7e+16], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0999999999999998e48 or 7e16 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.3%

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

   if -2.0999999999999998e48 < y < 7e16

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 77.9%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+48}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.8e+46) 1.0 (if (<= y 1.35e-6) (/ x (- 1.0 y)) (/ y (+ y -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.8e+46) {
		tmp = 1.0;
	} else if (y <= 1.35e-6) {
		tmp = x / (1.0 - y);
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-5.8d+46)) then
        tmp = 1.0d0
    else if (y <= 1.35d-6) then
        tmp = x / (1.0d0 - y)
    else
        tmp = y / (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.8e+46) {
		tmp = 1.0;
	} else if (y <= 1.35e-6) {
		tmp = x / (1.0 - y);
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.8e+46:
		tmp = 1.0
	elif y <= 1.35e-6:
		tmp = x / (1.0 - y)
	else:
		tmp = y / (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.8e+46)
		tmp = 1.0;
	elseif (y <= 1.35e-6)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = Float64(y / Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.8e+46)
		tmp = 1.0;
	elseif (y <= 1.35e-6)
		tmp = x / (1.0 - y);
	else
		tmp = y / (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.8e+46], 1.0, If[LessEqual[y, 1.35e-6], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8000000000000004e46

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 83.9%

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

   if -5.8000000000000004e46 < y < 1.34999999999999999e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.9%

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

   if 1.34999999999999999e-6 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.5%

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

      1. metadata-eval 75.5%

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

      2. times-frac 75.5%

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

      3. *-lft-identity 75.5%

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

      4. neg-mul-1 75.5%

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

      5. neg-sub0 75.5%

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

      6. associate--r- 75.5%

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

      7. metadata-eval 75.5%

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

   4. Simplified 75.5%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]

Alternative 5: 74.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -980:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -980.0) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -980.0) {
		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 <= (-980.0d0)) 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 <= -980.0) {
		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 <= -980.0:
		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 <= -980.0)
		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 <= -980.0)
		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, -980.0], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -980 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 74.9%

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

   if -980 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.1%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -980:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 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. Taylor expanded in y around inf 42.0%

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

3. Final simplification 42.0%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023285 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))