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

Percentage Accurate: 65.3% → 99.8%

Time: 11.5s

Alternatives: 12

Speedup: 1.0×

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: 65.3% 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: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -88000000000:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 12000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{1 - x}{-1 - y}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(x + -1\right) + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -88000000000.0)
   (+ x (/ (- 1.0 x) y))
   (if (<= y 12000.0)
     (fma y (/ (- 1.0 x) (- -1.0 y)) 1.0)
     (- x (/ (+ (+ x -1.0) (/ (+ (- 1.0 x) (/ (+ x -1.0) y)) y)) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -88000000000.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 12000.0) {
		tmp = fma(y, ((1.0 - x) / (-1.0 - y)), 1.0);
	} else {
		tmp = x - (((x + -1.0) + (((1.0 - x) + ((x + -1.0) / y)) / y)) / y);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -88000000000.0)
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	elseif (y <= 12000.0)
		tmp = fma(y, Float64(Float64(1.0 - x) / Float64(-1.0 - y)), 1.0);
	else
		tmp = Float64(x - Float64(Float64(Float64(x + -1.0) + Float64(Float64(Float64(1.0 - x) + Float64(Float64(x + -1.0) / y)) / y)) / y));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -88000000000.0], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 12000.0], N[(y * N[(N[(1.0 - x), $MachinePrecision] / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(x - N[(N[(N[(x + -1.0), $MachinePrecision] + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.8e10

   1. Initial program 35.8%

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

      1. associate-/l* 64.4%

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

      2. remove-double-neg 64.4%

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

      3. remove-double-neg 64.4%

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

      4. +-commutative 64.4%

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

   3. Simplified 64.4%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

   if -8.8e10 < y < 12000

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. fma-define 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

      11. unsub-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{1 - x}{-1 - y}, 1\right)} \]
   4. Add Preprocessing

   if 12000 < y

   1. Initial program 26.5%

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

      1. associate-/l* 46.3%

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

      2. remove-double-neg 46.3%

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

      3. remove-double-neg 46.3%

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

      4. +-commutative 46.3%

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

   3. Simplified 46.3%

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

   5. Taylor expanded in y around -inf 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -88000000000:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 12000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{1 - x}{-1 - y}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(x + -1\right) + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{if}\;t\_0 \leq 0.99998 \lor \neg \left(t\_0 \leq 40\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - \left(x + \frac{1 - x}{y}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ y 1.0))))
   (if (or (<= t_0 0.99998) (not (<= t_0 40.0)))
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (+ x (/ (- 1.0 (+ x (/ (- 1.0 x) y))) y)))))

C

double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 0.99998) || !(t_0 <= 40.0)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + ((1.0 - (x + ((1.0 - x) / y))) / 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 = (y * (1.0d0 - x)) / (y + 1.0d0)
    if ((t_0 <= 0.99998d0) .or. (.not. (t_0 <= 40.0d0))) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else
        tmp = x + ((1.0d0 - (x + ((1.0d0 - x) / y))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 0.99998) || !(t_0 <= 40.0)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + ((1.0 - (x + ((1.0 - x) / y))) / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (1.0 - x)) / (y + 1.0)
	tmp = 0
	if (t_0 <= 0.99998) or not (t_0 <= 40.0):
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	else:
		tmp = x + ((1.0 - (x + ((1.0 - x) / y))) / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(1.0 - x)) / Float64(y + 1.0))
	tmp = 0.0
	if ((t_0 <= 0.99998) || !(t_0 <= 40.0))
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	else
		tmp = Float64(x + Float64(Float64(1.0 - Float64(x + Float64(Float64(1.0 - x) / y))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * (1.0 - x)) / (y + 1.0);
	tmp = 0.0;
	if ((t_0 <= 0.99998) || ~((t_0 <= 40.0)))
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	else
		tmp = x + ((1.0 - (x + ((1.0 - x) / y))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.99998], N[Not[LessEqual[t$95$0, 40.0]], $MachinePrecision]], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 - N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.99997999999999998 or 40 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 83.9%

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

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. remove-double-neg 99.9%

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

      4. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   if 0.99997999999999998 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 40

   1. Initial program 6.4%

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

      1. associate-/l* 6.4%

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

      2. remove-double-neg 6.4%

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

      3. remove-double-neg 6.4%

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

      4. +-commutative 6.4%

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

   3. Simplified 6.4%

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

   5. Taylor expanded in y around inf 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 0.99998 \lor \neg \left(\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 40\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - \left(x + \frac{1 - x}{y}\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{if}\;t\_0 \leq 0.99998 \lor \neg \left(t\_0 \leq 40\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ y 1.0))))
   (if (or (<= t_0 0.99998) (not (<= t_0 40.0)))
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (+ x (/ (- 1.0 x) y)))))

C

double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 0.99998) || !(t_0 <= 40.0)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} 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 = (y * (1.0d0 - x)) / (y + 1.0d0)
    if ((t_0 <= 0.99998d0) .or. (.not. (t_0 <= 40.0d0))) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    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 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 0.99998) || !(t_0 <= 40.0)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (1.0 - x)) / (y + 1.0)
	tmp = 0
	if (t_0 <= 0.99998) or not (t_0 <= 40.0):
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	else:
		tmp = x + ((1.0 - x) / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(1.0 - x)) / Float64(y + 1.0))
	tmp = 0.0
	if ((t_0 <= 0.99998) || !(t_0 <= 40.0))
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	else
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * (1.0 - x)) / (y + 1.0);
	tmp = 0.0;
	if ((t_0 <= 0.99998) || ~((t_0 <= 40.0)))
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	else
		tmp = x + ((1.0 - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.99998], N[Not[LessEqual[t$95$0, 40.0]], $MachinePrecision]], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $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 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.99997999999999998 or 40 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 83.9%

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

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. remove-double-neg 99.9%

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

      4. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   if 0.99997999999999998 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 40

   1. Initial program 6.4%

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

      1. associate-/l* 6.4%

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

      2. remove-double-neg 6.4%

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

      3. remove-double-neg 6.4%

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

      4. +-commutative 6.4%

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

   3. Simplified 6.4%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. div-sub 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 0.99998 \lor \neg \left(\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 40\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -88000000000:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 12500:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(x + -1\right) + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -88000000000.0)
   (+ x (/ (- 1.0 x) y))
   (if (<= y 12500.0)
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (- x (/ (+ (+ x -1.0) (/ (+ (- 1.0 x) (/ (+ x -1.0) y)) y)) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -88000000000.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 12500.0) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x - (((x + -1.0) + (((1.0 - x) + ((x + -1.0) / y)) / y)) / 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 <= (-88000000000.0d0)) then
        tmp = x + ((1.0d0 - x) / y)
    else if (y <= 12500.0d0) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else
        tmp = x - (((x + (-1.0d0)) + (((1.0d0 - x) + ((x + (-1.0d0)) / y)) / y)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -88000000000.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 12500.0) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x - (((x + -1.0) + (((1.0 - x) + ((x + -1.0) / y)) / y)) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -88000000000.0:
		tmp = x + ((1.0 - x) / y)
	elif y <= 12500.0:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	else:
		tmp = x - (((x + -1.0) + (((1.0 - x) + ((x + -1.0) / y)) / y)) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -88000000000.0)
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	elseif (y <= 12500.0)
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	else
		tmp = Float64(x - Float64(Float64(Float64(x + -1.0) + Float64(Float64(Float64(1.0 - x) + Float64(Float64(x + -1.0) / y)) / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -88000000000.0)
		tmp = x + ((1.0 - x) / y);
	elseif (y <= 12500.0)
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	else
		tmp = x - (((x + -1.0) + (((1.0 - x) + ((x + -1.0) / y)) / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -88000000000.0], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 12500.0], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(x + -1.0), $MachinePrecision] + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.8e10

   1. Initial program 35.8%

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

      1. associate-/l* 64.4%

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

      2. remove-double-neg 64.4%

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

      3. remove-double-neg 64.4%

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

      4. +-commutative 64.4%

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

   3. Simplified 64.4%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

   if -8.8e10 < y < 12500

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   if 12500 < y

   1. Initial program 26.5%

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

      1. associate-/l* 46.3%

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

      2. remove-double-neg 46.3%

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

      3. remove-double-neg 46.3%

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

      4. +-commutative 46.3%

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

   3. Simplified 46.3%

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

   5. Taylor expanded in y around -inf 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -88000000000:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 12500:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(x + -1\right) + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-77}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-140}:\\ \;\;\;\;y \cdot \frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 31500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- x (/ x y))))
   (if (<= y -1.0)
     t_0
     (if (<= y -1.45e-77)
       (- 1.0 y)
       (if (<= y -1.1e-140)
         (* y (/ x (+ y 1.0)))
         (if (<= y 31500.0) 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = x - (x / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -1.45e-77) {
		tmp = 1.0 - y;
	} else if (y <= -1.1e-140) {
		tmp = y * (x / (y + 1.0));
	} else if (y <= 31500.0) {
		tmp = 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 = x - (x / y)
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= (-1.45d-77)) then
        tmp = 1.0d0 - y
    else if (y <= (-1.1d-140)) then
        tmp = y * (x / (y + 1.0d0))
    else if (y <= 31500.0d0) then
        tmp = 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x - (x / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -1.45e-77) {
		tmp = 1.0 - y;
	} else if (y <= -1.1e-140) {
		tmp = y * (x / (y + 1.0));
	} else if (y <= 31500.0) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x - (x / y)
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= -1.45e-77:
		tmp = 1.0 - y
	elif y <= -1.1e-140:
		tmp = y * (x / (y + 1.0))
	elif y <= 31500.0:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x - Float64(x / y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= -1.45e-77)
		tmp = Float64(1.0 - y);
	elseif (y <= -1.1e-140)
		tmp = Float64(y * Float64(x / Float64(y + 1.0)));
	elseif (y <= 31500.0)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x - (x / y);
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= -1.45e-77)
		tmp = 1.0 - y;
	elseif (y <= -1.1e-140)
		tmp = y * (x / (y + 1.0));
	elseif (y <= 31500.0)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, -1.45e-77], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, -1.1e-140], N[(y * N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 31500.0], 1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1 or 31500 < y

   1. Initial program 30.9%

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

      1. associate-/l* 54.6%

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

      2. remove-double-neg 54.6%

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

      3. remove-double-neg 54.6%

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

      4. +-commutative 54.6%

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

   3. Simplified 54.6%

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

   5. Taylor expanded in x around inf 51.9%

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

      1. *-commutative 51.9%

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

      2. associate-/l* 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in y around inf 75.7%

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

      1. mul-1-neg 75.7%

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

      2. unsub-neg 75.7%

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

   10. Simplified 75.7%

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

   if -1 < y < -1.4499999999999999e-77

   1. Initial program 99.9%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 67.4%

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

   6. Taylor expanded in y around 0 67.4%

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

      1. neg-mul-1 67.4%

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

      2. unsub-neg 67.4%

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

   8. Simplified 67.4%

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

   if -1.4499999999999999e-77 < y < -1.1e-140

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. associate-/l* 70.5%

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

   7. Simplified 70.5%

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

   if -1.1e-140 < y < 31500

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

      2. remove-double-neg 99.7%

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

      3. remove-double-neg 99.7%

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

      4. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 74.8%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x - \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-77}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-140}:\\ \;\;\;\;y \cdot \frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 31500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-75}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-140}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 31500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- x (/ x y))))
   (if (<= y -1.0)
     t_0
     (if (<= y -1.2e-75)
       (- 1.0 y)
       (if (<= y -1.6e-140) (* y x) (if (<= y 31500.0) 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = x - (x / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -1.2e-75) {
		tmp = 1.0 - y;
	} else if (y <= -1.6e-140) {
		tmp = y * x;
	} else if (y <= 31500.0) {
		tmp = 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 = x - (x / y)
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= (-1.2d-75)) then
        tmp = 1.0d0 - y
    else if (y <= (-1.6d-140)) then
        tmp = y * x
    else if (y <= 31500.0d0) then
        tmp = 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x - (x / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -1.2e-75) {
		tmp = 1.0 - y;
	} else if (y <= -1.6e-140) {
		tmp = y * x;
	} else if (y <= 31500.0) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x - (x / y)
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= -1.2e-75:
		tmp = 1.0 - y
	elif y <= -1.6e-140:
		tmp = y * x
	elif y <= 31500.0:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x - Float64(x / y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= -1.2e-75)
		tmp = Float64(1.0 - y);
	elseif (y <= -1.6e-140)
		tmp = Float64(y * x);
	elseif (y <= 31500.0)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x - (x / y);
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= -1.2e-75)
		tmp = 1.0 - y;
	elseif (y <= -1.6e-140)
		tmp = y * x;
	elseif (y <= 31500.0)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, -1.2e-75], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, -1.6e-140], N[(y * x), $MachinePrecision], If[LessEqual[y, 31500.0], 1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1 or 31500 < y

   1. Initial program 30.9%

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

      1. associate-/l* 54.6%

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

      2. remove-double-neg 54.6%

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

      3. remove-double-neg 54.6%

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

      4. +-commutative 54.6%

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

   3. Simplified 54.6%

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

   5. Taylor expanded in x around inf 51.9%

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

      1. *-commutative 51.9%

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

      2. associate-/l* 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in y around inf 75.7%

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

      1. mul-1-neg 75.7%

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

      2. unsub-neg 75.7%

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

   10. Simplified 75.7%

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

   if -1 < y < -1.2000000000000001e-75

   1. Initial program 99.9%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 67.4%

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

   6. Taylor expanded in y around 0 67.4%

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

      1. neg-mul-1 67.4%

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

      2. unsub-neg 67.4%

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

   8. Simplified 67.4%

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

   if -1.2000000000000001e-75 < y < -1.6000000000000001e-140

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. associate-/l* 70.5%

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

   7. Simplified 70.5%

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

   8. Taylor expanded in y around 0 70.5%

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

   if -1.6000000000000001e-140 < y < 31500

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

      2. remove-double-neg 99.7%

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

      3. remove-double-neg 99.7%

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

      4. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 74.8%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x - \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-75}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-140}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 31500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-76}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-140}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 31500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y -2.5e-76)
     (- 1.0 y)
     (if (<= y -1.6e-140) (* y x) (if (<= y 31500.0) 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= -2.5e-76) {
		tmp = 1.0 - y;
	} else if (y <= -1.6e-140) {
		tmp = y * x;
	} else if (y <= 31500.0) {
		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 <= (-2.5d-76)) then
        tmp = 1.0d0 - y
    else if (y <= (-1.6d-140)) then
        tmp = y * x
    else if (y <= 31500.0d0) 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 <= -2.5e-76) {
		tmp = 1.0 - y;
	} else if (y <= -1.6e-140) {
		tmp = y * x;
	} else if (y <= 31500.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= -2.5e-76:
		tmp = 1.0 - y
	elif y <= -1.6e-140:
		tmp = y * x
	elif y <= 31500.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= -2.5e-76)
		tmp = Float64(1.0 - y);
	elseif (y <= -1.6e-140)
		tmp = Float64(y * x);
	elseif (y <= 31500.0)
		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 <= -2.5e-76)
		tmp = 1.0 - y;
	elseif (y <= -1.6e-140)
		tmp = y * x;
	elseif (y <= 31500.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, -2.5e-76], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, -1.6e-140], N[(y * x), $MachinePrecision], If[LessEqual[y, 31500.0], 1.0, x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1 or 31500 < y

   1. Initial program 30.9%

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

      1. associate-/l* 54.6%

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

      2. remove-double-neg 54.6%

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

      3. remove-double-neg 54.6%

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

      4. +-commutative 54.6%

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

   3. Simplified 54.6%

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

   5. Taylor expanded in y around inf 75.3%

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

   if -1 < y < -2.4999999999999999e-76

   1. Initial program 99.9%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 67.4%

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

   6. Taylor expanded in y around 0 67.4%

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

      1. neg-mul-1 67.4%

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

      2. unsub-neg 67.4%

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

   8. Simplified 67.4%

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

   if -2.4999999999999999e-76 < y < -1.6000000000000001e-140

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. associate-/l* 70.5%

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

   7. Simplified 70.5%

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

   8. Taylor expanded in y around 0 70.5%

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

   if -1.6000000000000001e-140 < y < 31500

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

      2. remove-double-neg 99.7%

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

      3. remove-double-neg 99.7%

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

      4. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 74.8%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-76}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-140}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 31500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-76}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-140}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 31500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y -1.5e-76)
     1.0
     (if (<= y -1.6e-140) (* y x) (if (<= y 31500.0) 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= -1.5e-76) {
		tmp = 1.0;
	} else if (y <= -1.6e-140) {
		tmp = y * x;
	} else if (y <= 31500.0) {
		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 <= (-1.5d-76)) then
        tmp = 1.0d0
    else if (y <= (-1.6d-140)) then
        tmp = y * x
    else if (y <= 31500.0d0) 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 <= -1.5e-76) {
		tmp = 1.0;
	} else if (y <= -1.6e-140) {
		tmp = y * x;
	} else if (y <= 31500.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= -1.5e-76:
		tmp = 1.0
	elif y <= -1.6e-140:
		tmp = y * x
	elif y <= 31500.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= -1.5e-76)
		tmp = 1.0;
	elseif (y <= -1.6e-140)
		tmp = Float64(y * x);
	elseif (y <= 31500.0)
		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 <= -1.5e-76)
		tmp = 1.0;
	elseif (y <= -1.6e-140)
		tmp = y * x;
	elseif (y <= 31500.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, -1.5e-76], 1.0, If[LessEqual[y, -1.6e-140], N[(y * x), $MachinePrecision], If[LessEqual[y, 31500.0], 1.0, x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 31500 < y

   1. Initial program 30.9%

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

      1. associate-/l* 54.6%

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

      2. remove-double-neg 54.6%

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

      3. remove-double-neg 54.6%

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

      4. +-commutative 54.6%

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

   3. Simplified 54.6%

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

   5. Taylor expanded in y around inf 75.3%

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

   if -1 < y < -1.50000000000000012e-76 or -1.6000000000000001e-140 < y < 31500

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. remove-double-neg 99.8%

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

      3. remove-double-neg 99.8%

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

      4. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 74.0%

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

   if -1.50000000000000012e-76 < y < -1.6000000000000001e-140

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. associate-/l* 70.5%

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

   7. Simplified 70.5%

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

   8. Taylor expanded in y around 0 70.5%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-76}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-140}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 31500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.4% accurate, 0.6× speedup

Math

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

FPCore

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

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 * (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 <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 - (y * (1.0d0 - x))
    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 * (1.0 - x));
	}
	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 * (1.0 - x))
	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(1.0 - x)));
	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 * (1.0 - x));
	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[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 31.8%

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

      1. associate-/l* 55.1%

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

      2. remove-double-neg 55.1%

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

      3. remove-double-neg 55.1%

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

      4. +-commutative 55.1%

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

   3. Simplified 55.1%

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

   5. Taylor expanded in y around inf 98.9%

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

      1. associate--l+ 98.9%

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

      2. div-sub 98.9%

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

   7. Simplified 98.9%

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

   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. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.4%

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

4. Final simplification 99.2%

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

Alternative 10: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.96\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.96))) (+ x (/ (- 1.0 x) y)) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.96)) {
		tmp = x + ((1.0 - x) / 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 <= 0.96d0))) then
        tmp = x + ((1.0d0 - x) / 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 <= 0.96)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.96):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.96))
		tmp = Float64(x + Float64(Float64(1.0 - x) / 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 <= 0.96)))
		tmp = x + ((1.0 - x) / 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, 0.96]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.95999999999999996 < y

   1. Initial program 31.8%

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

      1. associate-/l* 55.1%

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

      2. remove-double-neg 55.1%

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

      3. remove-double-neg 55.1%

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

      4. +-commutative 55.1%

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

   3. Simplified 55.1%

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

   5. Taylor expanded in y around inf 98.9%

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

      1. associate--l+ 98.9%

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

      2. div-sub 98.9%

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

   7. Simplified 98.9%

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

   if -1 < y < 0.95999999999999996

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 70.7%

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

   6. Taylor expanded in y around 0 70.7%

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

      1. neg-mul-1 70.7%

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

      2. unsub-neg 70.7%

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

   8. Simplified 70.7%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.96\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 31500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 31500.0) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 31500.0) {
		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 <= 31500.0d0) 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 <= 31500.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 31500.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 31500.0)
		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 <= 31500.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 31500.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 31500 < y

   1. Initial program 30.9%

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

      1. associate-/l* 54.6%

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

      2. remove-double-neg 54.6%

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

      3. remove-double-neg 54.6%

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

      4. +-commutative 54.6%

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

   3. Simplified 54.6%

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

   5. Taylor expanded in y around inf 75.3%

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

   if -1 < y < 31500

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. remove-double-neg 99.8%

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

      3. remove-double-neg 99.8%

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

      4. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 69.7%

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

Alternative 12: 38.3% 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 64.8%

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

   1. associate-/l* 76.9%

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

   2. remove-double-neg 76.9%

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

   3. remove-double-neg 76.9%

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

   4. +-commutative 76.9%

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

3. Simplified 76.9%

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

5. Taylor expanded in y around 0 36.2%

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

Developer target: 99.7% accurate, 0.5× 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 2024100 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :alt
  (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))))