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

Percentage Accurate: 66.4% → 99.7%

Time: 10.1s

Alternatives: 9

Speedup: 2.1×

Specification

Math

\[\begin{array}{l} \\ 1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{1 + y}\\ \mathbf{if}\;t_0 \leq 0.05 \lor \neg \left(t_0 \leq 2\right):\\ \;\;\;\;1 + \frac{y}{1 + y} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\frac{1 - x}{{y}^{2}} + \left(\frac{x + -1}{y} + \frac{x + -1}{{y}^{3}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (- 1.0 x) y) (+ 1.0 y))))
   (if (or (<= t_0 0.05) (not (<= t_0 2.0)))
     (+ 1.0 (* (/ y (+ 1.0 y)) (+ x -1.0)))
     (-
      x
      (+
       (/ (- 1.0 x) (pow y 2.0))
       (+ (/ (+ x -1.0) y) (/ (+ x -1.0) (pow y 3.0))))))))

C

double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double tmp;
	if ((t_0 <= 0.05) || !(t_0 <= 2.0)) {
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	} else {
		tmp = x - (((1.0 - x) / pow(y, 2.0)) + (((x + -1.0) / y) + ((x + -1.0) / pow(y, 3.0))));
	}
	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) / (1.0d0 + y)
    if ((t_0 <= 0.05d0) .or. (.not. (t_0 <= 2.0d0))) then
        tmp = 1.0d0 + ((y / (1.0d0 + y)) * (x + (-1.0d0)))
    else
        tmp = x - (((1.0d0 - x) / (y ** 2.0d0)) + (((x + (-1.0d0)) / y) + ((x + (-1.0d0)) / (y ** 3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double tmp;
	if ((t_0 <= 0.05) || !(t_0 <= 2.0)) {
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	} else {
		tmp = x - (((1.0 - x) / Math.pow(y, 2.0)) + (((x + -1.0) / y) + ((x + -1.0) / Math.pow(y, 3.0))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((1.0 - x) * y) / (1.0 + y)
	tmp = 0
	if (t_0 <= 0.05) or not (t_0 <= 2.0):
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0))
	else:
		tmp = x - (((1.0 - x) / math.pow(y, 2.0)) + (((x + -1.0) / y) + ((x + -1.0) / math.pow(y, 3.0))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(1.0 - x) * y) / Float64(1.0 + y))
	tmp = 0.0
	if ((t_0 <= 0.05) || !(t_0 <= 2.0))
		tmp = Float64(1.0 + Float64(Float64(y / Float64(1.0 + y)) * Float64(x + -1.0)));
	else
		tmp = Float64(x - Float64(Float64(Float64(1.0 - x) / (y ^ 2.0)) + Float64(Float64(Float64(x + -1.0) / y) + Float64(Float64(x + -1.0) / (y ^ 3.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((1.0 - x) * y) / (1.0 + y);
	tmp = 0.0;
	if ((t_0 <= 0.05) || ~((t_0 <= 2.0)))
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	else
		tmp = x - (((1.0 - x) / (y ^ 2.0)) + (((x + -1.0) / y) + ((x + -1.0) / (y ^ 3.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.05], N[Not[LessEqual[t$95$0, 2.0]], $MachinePrecision]], N[(1.0 + N[(N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(1.0 - x), $MachinePrecision] / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)) < 0.050000000000000003 or 2 < (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

   1. Initial program 85.5%

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

      1. *-commutative 85.5%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   if 0.050000000000000003 < (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)) < 2

   1. Initial program 9.1%

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

      1. *-commutative 9.1%

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

      2. associate-*l/ 9.1%

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

      3. +-commutative 9.1%

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

   3. Simplified 9.1%

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

   4. Taylor expanded in y around -inf 99.6%

      \[\leadsto \color{blue}{\left(x + \left(-1 \cdot \frac{x - 1}{y} + \left(-1 \cdot \frac{x - 1}{{y}^{3}} + \frac{x}{{y}^{2}}\right)\right)\right) - \frac{1}{{y}^{2}}} \]
   5. Step-by-step derivation

      1. associate--l+ 99.6%

         \[\leadsto \color{blue}{x + \left(\left(-1 \cdot \frac{x - 1}{y} + \left(-1 \cdot \frac{x - 1}{{y}^{3}} + \frac{x}{{y}^{2}}\right)\right) - \frac{1}{{y}^{2}}\right)} \]

      2. associate-+r+ 99.6%

         \[\leadsto x + \left(\color{blue}{\left(\left(-1 \cdot \frac{x - 1}{y} + -1 \cdot \frac{x - 1}{{y}^{3}}\right) + \frac{x}{{y}^{2}}\right)} - \frac{1}{{y}^{2}}\right) \]

      3. associate--l+ 99.6%

         \[\leadsto x + \color{blue}{\left(\left(-1 \cdot \frac{x - 1}{y} + -1 \cdot \frac{x - 1}{{y}^{3}}\right) + \left(\frac{x}{{y}^{2}} - \frac{1}{{y}^{2}}\right)\right)} \]

   6. Simplified 99.6%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 0.05 \lor \neg \left(\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 2\right):\\ \;\;\;\;1 + \frac{y}{1 + y} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\frac{1 - x}{{y}^{2}} + \left(\frac{x + -1}{y} + \frac{x + -1}{{y}^{3}}\right)\right)\\ \end{array} \]

Alternative 2: 99.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{1 + y}\\ \mathbf{if}\;t_0 \leq 0.99996 \lor \neg \left(t_0 \leq 1\right):\\ \;\;\;\;1 + \frac{y}{1 + y} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (- 1.0 x) y) (+ 1.0 y))))
   (if (or (<= t_0 0.99996) (not (<= t_0 1.0)))
     (+ 1.0 (* (/ y (+ 1.0 y)) (+ x -1.0)))
     (+ x (/ (- 1.0 x) y)))))

C

double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double tmp;
	if ((t_0 <= 0.99996) || !(t_0 <= 1.0)) {
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	} else {
		tmp = x + ((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) :: t_0
    real(8) :: tmp
    t_0 = ((1.0d0 - x) * y) / (1.0d0 + y)
    if ((t_0 <= 0.99996d0) .or. (.not. (t_0 <= 1.0d0))) then
        tmp = 1.0d0 + ((y / (1.0d0 + y)) * (x + (-1.0d0)))
    else
        tmp = x + ((1.0d0 - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double tmp;
	if ((t_0 <= 0.99996) || !(t_0 <= 1.0)) {
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((1.0 - x) * y) / (1.0 + y)
	tmp = 0
	if (t_0 <= 0.99996) or not (t_0 <= 1.0):
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0))
	else:
		tmp = x + ((1.0 - x) / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(1.0 - x) * y) / Float64(1.0 + y))
	tmp = 0.0
	if ((t_0 <= 0.99996) || !(t_0 <= 1.0))
		tmp = Float64(1.0 + Float64(Float64(y / Float64(1.0 + y)) * Float64(x + -1.0)));
	else
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((1.0 - x) * y) / (1.0 + y);
	tmp = 0.0;
	if ((t_0 <= 0.99996) || ~((t_0 <= 1.0)))
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	else
		tmp = x + ((1.0 - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.99996], N[Not[LessEqual[t$95$0, 1.0]], $MachinePrecision]], N[(1.0 + N[(N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)) < 0.99995999999999996 or 1 < (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

   1. Initial program 85.4%

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

      1. *-commutative 85.4%

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

      2. associate-*l/ 99.7%

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

      3. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   if 0.99995999999999996 < (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)) < 1

   1. Initial program 5.5%

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

      1. *-commutative 5.5%

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

      2. associate-*l/ 5.5%

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

      3. +-commutative 5.5%

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

   3. Simplified 5.5%

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

   4. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 0.99996 \lor \neg \left(\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 1\right):\\ \;\;\;\;1 + \frac{y}{1 + y} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \]

Alternative 3: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.78\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.78)))
   (- x (/ -1.0 y))
   (+ 1.0 (* y (+ x -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.78)) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 1.0 + (y * (x + -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 <= (-1.0d0)) .or. (.not. (y <= 0.78d0))) then
        tmp = x - ((-1.0d0) / y)
    else
        tmp = 1.0d0 + (y * (x + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.78)) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 1.0 + (y * (x + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.78):
		tmp = x - (-1.0 / y)
	else:
		tmp = 1.0 + (y * (x + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.78))
		tmp = Float64(x - Float64(-1.0 / y));
	else
		tmp = Float64(1.0 + Float64(y * Float64(x + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.78)))
		tmp = x - (-1.0 / y);
	else
		tmp = 1.0 + (y * (x + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.78]], $MachinePrecision]], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.78000000000000003 < y

   1. Initial program 37.0%

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

      1. *-commutative 37.0%

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

      2. associate-*l/ 57.9%

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

      3. +-commutative 57.9%

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

   3. Simplified 57.9%

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

   4. Taylor expanded in y around -inf 98.0%

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

      1. mul-1-neg 98.0%

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

      2. unsub-neg 98.0%

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

      3. sub-neg 98.0%

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

      4. metadata-eval 98.0%

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

   6. Simplified 98.0%

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

   7. Taylor expanded in x around 0 97.3%

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

   if -1 < y < 0.78000000000000003

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.9%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.78\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 4: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 37.0%

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

      1. *-commutative 37.0%

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

      2. associate-*l/ 57.9%

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

      3. +-commutative 57.9%

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

   3. Simplified 57.9%

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

   4. Taylor expanded in y around -inf 98.0%

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

      1. mul-1-neg 98.0%

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

      2. unsub-neg 98.0%

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

      3. sub-neg 98.0%

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

      4. metadata-eval 98.0%

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

   6. Simplified 98.0%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.9%

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

4. Final simplification 98.4%

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

Alternative 5: 86.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.12\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.12))) (- x (/ -1.0 y)) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.12)) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 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 <= (-1.0d0)) .or. (.not. (y <= 0.12d0))) then
        tmp = x - ((-1.0d0) / y)
    else
        tmp = 1.0d0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.12)) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.12):
		tmp = x - (-1.0 / y)
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.12))
		tmp = Float64(x - Float64(-1.0 / y));
	else
		tmp = Float64(1.0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.12)))
		tmp = x - (-1.0 / y);
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.12]], $MachinePrecision]], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.12 < y

   1. Initial program 37.0%

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

      1. *-commutative 37.0%

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

      2. associate-*l/ 57.9%

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

      3. +-commutative 57.9%

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

   3. Simplified 57.9%

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

   4. Taylor expanded in y around -inf 98.0%

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

      1. mul-1-neg 98.0%

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

      2. unsub-neg 98.0%

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

      3. sub-neg 98.0%

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

      4. metadata-eval 98.0%

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

   6. Simplified 98.0%

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

   7. Taylor expanded in x around 0 97.3%

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

   if -1 < y < 0.12

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.9%

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

   5. Taylor expanded in x around 0 78.4%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.12\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 6: 97.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 37.0%

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

      1. *-commutative 37.0%

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

      2. associate-*l/ 57.9%

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

      3. +-commutative 57.9%

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

   3. Simplified 57.9%

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

   4. Taylor expanded in y around -inf 98.0%

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

      1. mul-1-neg 98.0%

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

      2. unsub-neg 98.0%

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

      3. sub-neg 98.0%

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

      4. metadata-eval 98.0%

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

   6. Simplified 98.0%

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

   7. Taylor expanded in x around 0 97.3%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.9%

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

   5. Taylor expanded in x around inf 98.4%

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

      1. mul-1-neg 98.4%

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

      2. distribute-lft-neg-out 98.4%

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

      3. *-commutative 98.4%

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

   7. Simplified 98.4%

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

4. Final simplification 97.8%

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

Alternative 7: 74.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.58:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 0.58) (- 1.0 y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.58) {
		tmp = 1.0 - 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 <= (-1.0d0)) then
        tmp = x
    else if (y <= 0.58d0) then
        tmp = 1.0d0 - y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.58) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.58:
		tmp = 1.0 - y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.58)
		tmp = Float64(1.0 - y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.58)
		tmp = 1.0 - y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 0.58], N[(1.0 - y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.57999999999999996 < y

   1. Initial program 37.0%

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

      1. *-commutative 37.0%

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

      2. associate-*l/ 57.9%

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

      3. +-commutative 57.9%

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

   3. Simplified 57.9%

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

   4. Taylor expanded in y around inf 76.5%

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

   if -1 < y < 0.57999999999999996

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.9%

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

   5. Taylor expanded in x around 0 78.4%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.58:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 73.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.9:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 0.9) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.9) {
		tmp = 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 <= (-1.0d0)) then
        tmp = x
    else if (y <= 0.9d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.9) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.9:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.9)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.9)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 0.9], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.900000000000000022 < y

   1. Initial program 37.0%

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

      1. *-commutative 37.0%

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

      2. associate-*l/ 57.9%

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

      3. +-commutative 57.9%

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

   3. Simplified 57.9%

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

   4. Taylor expanded in y around inf 76.5%

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

   if -1 < y < 0.900000000000000022

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 77.9%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.9:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 39.6% accurate, 11.0× 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 67.0%

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

   1. *-commutative 67.0%

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

   2. associate-*l/ 78.0%

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

   3. +-commutative 78.0%

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

3. Simplified 78.0%

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

4. Taylor expanded in y around 0 39.1%

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

5. Final simplification 39.1%

   \[\leadsto 1 \]

Developer target: 99.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \mathbf{if}\;y < -3693.8482788297247:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y < 6799310503.41891:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (/ 1.0 y) (- (/ x y) x))))
   (if (< y -3693.8482788297247)
     t_0
     (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) t_0))))

C

double code(double x, double y) {
	double t_0 = (1.0 / y) - ((x / y) - x);
	double tmp;
	if (y < -3693.8482788297247) {
		tmp = t_0;
	} else if (y < 6799310503.41891) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} 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 / y) - ((x / y) - x)
    if (y < (-3693.8482788297247d0)) then
        tmp = t_0
    else if (y < 6799310503.41891d0) then
        tmp = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 / y) - ((x / y) - x);
	double tmp;
	if (y < -3693.8482788297247) {
		tmp = t_0;
	} else if (y < 6799310503.41891) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 / y) - ((x / y) - x)
	tmp = 0
	if y < -3693.8482788297247:
		tmp = t_0
	elif y < 6799310503.41891:
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 / y) - Float64(Float64(x / y) - x))
	tmp = 0.0
	if (y < -3693.8482788297247)
		tmp = t_0;
	elseif (y < 6799310503.41891)
		tmp = Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 / y) - ((x / y) - x);
	tmp = 0.0;
	if (y < -3693.8482788297247)
		tmp = t_0;
	elseif (y < 6799310503.41891)
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 / y), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -3693.8482788297247], t$95$0, If[Less[y, 6799310503.41891], N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023334 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ 1.0 y) (- (/ x y) x)) (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) (- (/ 1.0 y) (- (/ x y) x))))

  (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))