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

Percentage Accurate: 65.9% → 99.9%

Time: 13.3s

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: 65.9% 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: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -380000 \lor \neg \left(y \leq 430000\right):\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{1 - x}{-1 - y}, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -380000.0) (not (<= y 430000.0)))
   (+ x (/ (+ (- 1.0 x) (/ (+ x -1.0) y)) y))
   (fma y (/ (- 1.0 x) (- -1.0 y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -380000.0) || !(y <= 430000.0)) {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	} else {
		tmp = fma(y, ((1.0 - x) / (-1.0 - y)), 1.0);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -380000.0) || !(y <= 430000.0))
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(x + -1.0) / y)) / y));
	else
		tmp = fma(y, Float64(Float64(1.0 - x) / Float64(-1.0 - y)), 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -380000.0], N[Not[LessEqual[y, 430000.0]], $MachinePrecision]], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(1.0 - x), $MachinePrecision] / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8e5 or 4.3e5 < y

   1. Initial program 25.4%

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

      1. associate-/l* 56.0%

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

      2. remove-double-neg 56.0%

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

      3. remove-double-neg 56.0%

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

      4. +-commutative 56.0%

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

   3. Simplified 56.0%

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

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

   if -3.8e5 < y < 4.3e5

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-/l* 99.8%

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

      5. distribute-rgt-neg-in 99.8%

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

      6. fma-define 99.8%

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

      7. distribute-frac-neg2 99.8%

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

      8. +-commutative 99.8%

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

      9. distribute-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

      11. unsub-neg 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{1 - x}{-1 - y}, 1\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -380000 \lor \neg \left(y \leq 430000\right):\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{1 - x}{-1 - y}, 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{if}\;t\_0 \leq 0.5 \lor \neg \left(t\_0 \leq 1.002\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ y 1.0))))
   (if (or (<= t_0 0.5) (not (<= t_0 1.002)))
     (+ 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 <= 0.5) || !(t_0 <= 1.002)) {
		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 <= 0.5d0) .or. (.not. (t_0 <= 1.002d0))) 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 <= 0.5) || !(t_0 <= 1.002)) {
		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 <= 0.5) or not (t_0 <= 1.002):
		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 <= 0.5) || !(t_0 <= 1.002))
		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 <= 0.5) || ~((t_0 <= 1.002)))
		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, 0.5], N[Not[LessEqual[t$95$0, 1.002]], $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))) < 0.5 or 1.002 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 81.1%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   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 0.5 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1.002

   1. Initial program 5.8%

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

      1. associate-/l* 5.8%

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

      2. remove-double-neg 5.8%

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

      3. remove-double-neg 5.8%

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

      4. +-commutative 5.8%

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

   3. Simplified 5.8%

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

   5. Taylor expanded in y around inf 99.2%

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

      1. associate--l+ 99.2%

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

      2. div-sub 99.2%

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

   7. Simplified 99.2%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 0.5 \lor \neg \left(\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 1.002\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+29} \lor \neg \left(y \leq 2.9 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-1 + \left(y + y \cdot \left(-1 - x\right)\right)}{x}}{-1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.35e+29) (not (<= y 2.9e+15)))
   (+ x (/ (- 1.0 x) y))
   (* x (/ (/ (+ -1.0 (+ y (* y (- -1.0 x)))) x) (- -1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.35e+29) || !(y <= 2.9e+15)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = x * (((-1.0 + (y + (y * (-1.0 - x)))) / x) / (-1.0 - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2.35d+29)) .or. (.not. (y <= 2.9d+15))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = x * ((((-1.0d0) + (y + (y * ((-1.0d0) - x)))) / x) / ((-1.0d0) - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.35e+29) || !(y <= 2.9e+15)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = x * (((-1.0 + (y + (y * (-1.0 - x)))) / x) / (-1.0 - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.35e+29) or not (y <= 2.9e+15):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = x * (((-1.0 + (y + (y * (-1.0 - x)))) / x) / (-1.0 - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.35e+29) || !(y <= 2.9e+15))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(x * Float64(Float64(Float64(-1.0 + Float64(y + Float64(y * Float64(-1.0 - x)))) / x) / Float64(-1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.35e+29) || ~((y <= 2.9e+15)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = x * (((-1.0 + (y + (y * (-1.0 - x)))) / x) / (-1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.35e+29], N[Not[LessEqual[y, 2.9e+15]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(-1.0 + N[(y + N[(y * N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3500000000000001e29 or 2.9e15 < y

   1. Initial program 23.7%

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

      1. associate-/l* 56.4%

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

      2. remove-double-neg 56.4%

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

      3. remove-double-neg 56.4%

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

      4. +-commutative 56.4%

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

   3. Simplified 56.4%

      \[\leadsto \color{blue}{1 - \left(1 - x\right) \cdot \frac{y}{1 + y}} \]
   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 -2.3500000000000001e29 < y < 2.9e15

   1. Initial program 97.0%

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

      1. associate-/l* 97.0%

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

      2. remove-double-neg 97.0%

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

      3. remove-double-neg 97.0%

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

      4. +-commutative 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in x around inf 96.9%

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

      1. sub-neg 96.9%

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

      2. distribute-neg-in 96.9%

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

      3. add-sqr-sqrt 42.8%

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

      4. sqrt-unprod 76.5%

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

      5. mul-1-neg 76.5%

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

      6. mul-1-neg 76.5%

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

      7. sqr-neg 76.5%

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

      8. sqrt-unprod 35.9%

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

      9. add-sqr-sqrt 69.7%

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

      10. mul-1-neg 69.7%

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

      11. sub-neg 69.7%

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

      12. associate-*r/ 69.7%

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

      13. associate-/r* 69.8%

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

      14. sub-div 69.8%

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

      15. neg-mul-1 69.8%

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

   7. Applied egg-rr 69.8%

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

      1. frac-2neg 69.8%

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

      2. metadata-eval 69.8%

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

      3. frac-add 70.2%

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

   9. Applied egg-rr 97.4%

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

       1. cancel-sign-sub-inv 97.4%

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

       2. distribute-lft-neg-in 97.4%

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

       3. distribute-rgt-neg-in 97.4%

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

       4. associate-/r* 97.4%

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

   11. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+29} \lor \neg \left(y \leq 2.9 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-1 + \left(y + y \cdot \left(-1 - x\right)\right)}{x}}{-1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -255000 \lor \neg \left(y \leq 310000\right):\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -255000.0) (not (<= y 310000.0)))
   (+ x (/ (+ (- 1.0 x) (/ (+ x -1.0) y)) y))
   (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -255000.0) || !(y <= 310000.0)) {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	} else {
		tmp = 1.0 + ((1.0 - x) * (y / (-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 <= (-255000.0d0)) .or. (.not. (y <= 310000.0d0))) then
        tmp = x + (((1.0d0 - x) + ((x + (-1.0d0)) / y)) / y)
    else
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -255000.0) || !(y <= 310000.0)) {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	} else {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -255000.0) or not (y <= 310000.0):
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y)
	else:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -255000.0) || !(y <= 310000.0))
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(x + -1.0) / y)) / y));
	else
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -255000.0) || ~((y <= 310000.0)))
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	else
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -255000.0], N[Not[LessEqual[y, 310000.0]], $MachinePrecision]], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -255000 or 3.1e5 < y

   1. Initial program 25.4%

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

      1. associate-/l* 56.0%

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

      2. remove-double-neg 56.0%

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

      3. remove-double-neg 56.0%

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

      4. +-commutative 56.0%

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

   3. Simplified 56.0%

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

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

   if -255000 < y < 3.1e5

   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
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -255000 \lor \neg \left(y \leq 310000\right):\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - x \leq -50000000 \lor \neg \left(1 - x \leq 5 \cdot 10^{+44}\right):\\ \;\;\;\;x \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (- 1.0 x) -50000000.0) (not (<= (- 1.0 x) 5e+44)))
   (* x (/ y (+ y 1.0)))
   (/ 1.0 (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - x) <= -50000000.0) || !((1.0 - x) <= 5e+44)) {
		tmp = x * (y / (y + 1.0));
	} else {
		tmp = 1.0 / (y + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((1.0d0 - x) <= (-50000000.0d0)) .or. (.not. ((1.0d0 - x) <= 5d+44))) then
        tmp = x * (y / (y + 1.0d0))
    else
        tmp = 1.0d0 / (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((1.0 - x) <= -50000000.0) || !((1.0 - x) <= 5e+44)) {
		tmp = x * (y / (y + 1.0));
	} else {
		tmp = 1.0 / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - x) <= -50000000.0) or not ((1.0 - x) <= 5e+44):
		tmp = x * (y / (y + 1.0))
	else:
		tmp = 1.0 / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(1.0 - x) <= -50000000.0) || !(Float64(1.0 - x) <= 5e+44))
		tmp = Float64(x * Float64(y / Float64(y + 1.0)));
	else
		tmp = Float64(1.0 / Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((1.0 - x) <= -50000000.0) || ~(((1.0 - x) <= 5e+44)))
		tmp = x * (y / (y + 1.0));
	else
		tmp = 1.0 / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[(1.0 - x), $MachinePrecision], -50000000.0], N[Not[LessEqual[N[(1.0 - x), $MachinePrecision], 5e+44]], $MachinePrecision]], N[(x * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) x) < -5e7 or 4.9999999999999996e44 < (-.f64 #s(literal 1 binary64) x)

   1. Initial program 69.4%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   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 51.1%

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

      1. associate-/l* 81.6%

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

   7. Simplified 81.6%

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

   if -5e7 < (-.f64 #s(literal 1 binary64) x) < 4.9999999999999996e44

   1. Initial program 59.9%

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

      1. associate-/l* 60.6%

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

      2. remove-double-neg 60.6%

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

      3. remove-double-neg 60.6%

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

      4. +-commutative 60.6%

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

   3. Simplified 60.6%

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

   5. Taylor expanded in x around inf 60.8%

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

      1. sub-neg 60.8%

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

      2. distribute-neg-in 60.8%

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

      3. add-sqr-sqrt 26.2%

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

      4. sqrt-unprod 57.9%

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

      5. mul-1-neg 57.9%

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

      6. mul-1-neg 57.9%

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

      7. sqr-neg 57.9%

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

      8. sqrt-unprod 31.7%

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

      9. add-sqr-sqrt 57.9%

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

      10. mul-1-neg 57.9%

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

      11. sub-neg 57.9%

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

      12. associate-*r/ 57.9%

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

      13. associate-/r* 57.2%

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

      14. sub-div 57.2%

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

      15. neg-mul-1 57.2%

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

   7. Applied egg-rr 57.2%

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

      1. frac-2neg 57.2%

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

      2. metadata-eval 57.2%

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

      3. frac-add 57.4%

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

   9. Applied egg-rr 59.6%

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

       1. cancel-sign-sub-inv 59.6%

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

       2. distribute-lft-neg-in 59.6%

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

       3. distribute-rgt-neg-in 59.6%

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

       4. associate-/r* 59.7%

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

   11. Simplified 80.2%

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

   12. Taylor expanded in x around 0 78.4%

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

       1. +-commutative 78.4%

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

   14. Simplified 78.4%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - x \leq -50000000 \lor \neg \left(1 - x \leq 5 \cdot 10^{+44}\right):\\ \;\;\;\;x \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -66000000000 \lor \neg \left(y \leq 480000000000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -66000000000.0) (not (<= y 480000000000.0)))
   (+ x (/ (- 1.0 x) y))
   (/ 1.0 (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -66000000000.0) || !(y <= 480000000000.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 / (y + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-66000000000.0d0)) .or. (.not. (y <= 480000000000.0d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 / (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -66000000000.0) || !(y <= 480000000000.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -66000000000.0) or not (y <= 480000000000.0):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -66000000000.0) || !(y <= 480000000000.0))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(1.0 / Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -66000000000.0) || ~((y <= 480000000000.0)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = 1.0 / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -66000000000.0], N[Not[LessEqual[y, 480000000000.0]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.6e10 or 4.8e11 < y

   1. Initial program 25.1%

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

      1. associate-/l* 56.2%

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

      2. remove-double-neg 56.2%

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

      3. remove-double-neg 56.2%

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

      4. +-commutative 56.2%

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

   3. Simplified 56.2%

      \[\leadsto \color{blue}{1 - \left(1 - x\right) \cdot \frac{y}{1 + y}} \]
   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 -6.6e10 < y < 4.8e11

   1. Initial program 99.0%

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

      1. associate-/l* 99.0%

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

      2. remove-double-neg 99.0%

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

      3. remove-double-neg 99.0%

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

      4. +-commutative 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in x around inf 98.8%

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

      1. sub-neg 98.8%

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

      2. distribute-neg-in 98.8%

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

      3. add-sqr-sqrt 44.7%

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

      4. sqrt-unprod 79.8%

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

      5. mul-1-neg 79.8%

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

      6. mul-1-neg 79.8%

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

      7. sqr-neg 79.8%

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

      8. sqrt-unprod 37.3%

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

      9. add-sqr-sqrt 72.6%

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

      10. mul-1-neg 72.6%

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

      11. sub-neg 72.6%

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

      12. associate-*r/ 72.6%

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

      13. associate-/r* 72.7%

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

      14. sub-div 72.7%

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

      15. neg-mul-1 72.7%

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

   7. Applied egg-rr 72.7%

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

      1. frac-2neg 72.7%

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

      2. metadata-eval 72.7%

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

      3. frac-add 73.2%

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

   9. Applied egg-rr 99.4%

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

       1. cancel-sign-sub-inv 99.4%

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

       2. distribute-lft-neg-in 99.4%

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

       3. distribute-rgt-neg-in 99.4%

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

       4. associate-/r* 99.4%

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

   11. Simplified 99.8%

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

   12. Taylor expanded in x around 0 74.5%

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

       1. +-commutative 74.5%

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

   14. Simplified 74.5%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -66000000000 \lor \neg \left(y \leq 480000000000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.3% 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 28.1%

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

      1. associate-/l* 57.5%

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

      2. remove-double-neg 57.5%

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

      3. remove-double-neg 57.5%

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

      4. +-commutative 57.5%

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

   3. Simplified 57.5%

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

   5. Taylor expanded in y around inf 96.8%

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

      1. associate--l+ 96.8%

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

      2. div-sub 96.8%

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

   7. Simplified 96.8%

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

   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 98.0%

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

4. Final simplification 97.4%

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

Alternative 8: 73.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 28.1%

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

      1. associate-/l* 57.5%

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

      2. remove-double-neg 57.5%

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

      3. remove-double-neg 57.5%

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

      4. +-commutative 57.5%

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

   3. Simplified 57.5%

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

   5. Taylor expanded in x around inf 43.5%

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

      1. associate-/l* 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in y around inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. unsub-neg 71.8%

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

   10. Simplified 71.8%

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

   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 x around 0 74.6%

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

   6. Taylor expanded in y around 0 73.7%

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

      1. neg-mul-1 73.7%

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

      2. unsub-neg 73.7%

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

   8. Simplified 73.7%

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

4. Final simplification 72.8%

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

Alternative 9: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1300000000000:\\ \;\;\;\;\frac{1}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.15e+58)
   x
   (if (<= y 1300000000000.0) (/ 1.0 (+ y 1.0)) (- x (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.15e+58) {
		tmp = x;
	} else if (y <= 1300000000000.0) {
		tmp = 1.0 / (y + 1.0);
	} else {
		tmp = x - (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.15d+58)) then
        tmp = x
    else if (y <= 1300000000000.0d0) then
        tmp = 1.0d0 / (y + 1.0d0)
    else
        tmp = x - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.15e+58) {
		tmp = x;
	} else if (y <= 1300000000000.0) {
		tmp = 1.0 / (y + 1.0);
	} else {
		tmp = x - (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.15e+58:
		tmp = x
	elif y <= 1300000000000.0:
		tmp = 1.0 / (y + 1.0)
	else:
		tmp = x - (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.15e+58)
		tmp = x;
	elseif (y <= 1300000000000.0)
		tmp = Float64(1.0 / Float64(y + 1.0));
	else
		tmp = Float64(x - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.15e+58)
		tmp = x;
	elseif (y <= 1300000000000.0)
		tmp = 1.0 / (y + 1.0);
	else
		tmp = x - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.15e+58], x, If[LessEqual[y, 1300000000000.0], N[(1.0 / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15000000000000001e58

   1. Initial program 24.9%

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

      1. associate-/l* 58.5%

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

      2. remove-double-neg 58.5%

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

      3. remove-double-neg 58.5%

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

      4. +-commutative 58.5%

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

   3. Simplified 58.5%

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

   5. Taylor expanded in y around inf 78.2%

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

   if -1.15000000000000001e58 < y < 1.3e12

   1. Initial program 95.1%

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

      1. associate-/l* 95.7%

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

      2. remove-double-neg 95.7%

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

      3. remove-double-neg 95.7%

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

      4. +-commutative 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf 95.6%

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

      1. sub-neg 95.6%

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

      2. distribute-neg-in 95.6%

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

      3. add-sqr-sqrt 41.9%

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

      4. sqrt-unprod 75.0%

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

      5. mul-1-neg 75.0%

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

      6. mul-1-neg 75.0%

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

      7. sqr-neg 75.0%

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

      8. sqrt-unprod 35.2%

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

      9. add-sqr-sqrt 68.3%

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

      10. mul-1-neg 68.3%

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

      11. sub-neg 68.3%

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

      12. associate-*r/ 68.3%

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

      13. associate-/r* 68.4%

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

      14. sub-div 68.4%

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

      15. neg-mul-1 68.4%

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

   7. Applied egg-rr 68.4%

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

      1. frac-2neg 68.4%

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

      2. metadata-eval 68.4%

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

      3. frac-add 68.8%

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

   9. Applied egg-rr 95.4%

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

       1. cancel-sign-sub-inv 95.4%

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

       2. distribute-lft-neg-in 95.4%

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

       3. distribute-rgt-neg-in 95.4%

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

       4. associate-/r* 95.5%

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

   11. Simplified 99.2%

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

   12. Taylor expanded in x around 0 73.4%

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

       1. +-commutative 73.4%

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

   14. Simplified 73.4%

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

   if 1.3e12 < y

   1. Initial program 23.6%

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

      1. associate-/l* 55.6%

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

      2. remove-double-neg 55.6%

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

      3. remove-double-neg 55.6%

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

      4. +-commutative 55.6%

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

   3. Simplified 55.6%

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

   5. Taylor expanded in x around inf 45.1%

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

      1. associate-/l* 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in y around inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. unsub-neg 77.2%

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

   10. Simplified 77.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1300000000000:\\ \;\;\;\;\frac{1}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.88:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 0.88) (- 1.0 y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.88) {
		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 <= 0.88d0) 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 <= 0.88) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.88:
		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 <= 0.88)
		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 <= 0.88)
		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, 0.88], N[(1.0 - y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.880000000000000004 < y

   1. Initial program 28.1%

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

      1. associate-/l* 57.5%

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

      2. remove-double-neg 57.5%

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

      3. remove-double-neg 57.5%

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

      4. +-commutative 57.5%

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

   3. Simplified 57.5%

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

   5. Taylor expanded in y around inf 71.5%

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

   if -1 < y < 0.880000000000000004

   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 74.6%

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

   6. Taylor expanded in y around 0 73.7%

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

      1. neg-mul-1 73.7%

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

      2. unsub-neg 73.7%

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

   8. Simplified 73.7%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.88:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 480000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 480000000000.0) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 480000000000.0) {
		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 <= 480000000000.0d0) 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 <= 480000000000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 480000000000.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 480000000000.0)
		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 <= 480000000000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 480000000000.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 4.8e11 < y

   1. Initial program 28.0%

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

      1. associate-/l* 57.7%

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

      2. remove-double-neg 57.7%

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

      3. remove-double-neg 57.7%

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

      4. +-commutative 57.7%

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

   3. Simplified 57.7%

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

   5. Taylor expanded in y around inf 72.1%

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

   if -1 < y < 4.8e11

   1. Initial program 99.6%

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

      1. associate-/l* 99.5%

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

      2. remove-double-neg 99.5%

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

      3. remove-double-neg 99.5%

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

      4. +-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 73.0%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 480000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. 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 64.3%

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

   1. associate-/l* 78.9%

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

   2. remove-double-neg 78.9%

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

   3. remove-double-neg 78.9%

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

   4. +-commutative 78.9%

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

3. Simplified 78.9%

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

5. Taylor expanded in y around 0 38.7%

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

6. Final simplification 38.7%

   \[\leadsto 1 \]
7. 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 2024079 
(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))))