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

Percentage Accurate: 66.2% → 99.1%

Time: 7.5s

Alternatives: 11

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: 66.2% 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: 99.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{1 + y}\\ \mathbf{if}\;t\_0 \leq 0.2:\\ \;\;\;\;\mathsf{fma}\left(1 - x, \frac{y}{-1 - y}, 1\right)\\ \mathbf{elif}\;t\_0 \leq 500000000000:\\ \;\;\;\;x - \frac{\left(x + -1\right) + \frac{\left(1 - x\right) - \frac{1 - x}{y}}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{y}{1 + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ 1.0 y))))
   (if (<= t_0 0.2)
     (fma (- 1.0 x) (/ y (- -1.0 y)) 1.0)
     (if (<= t_0 500000000000.0)
       (- x (/ (+ (+ x -1.0) (/ (- (- 1.0 x) (/ (- 1.0 x) y)) y)) y))
       (+ 1.0 (* x (/ y (+ 1.0 y))))))))

C

double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (1.0 + y);
	double tmp;
	if (t_0 <= 0.2) {
		tmp = fma((1.0 - x), (y / (-1.0 - y)), 1.0);
	} else if (t_0 <= 500000000000.0) {
		tmp = x - (((x + -1.0) + (((1.0 - x) - ((1.0 - x) / y)) / y)) / y);
	} else {
		tmp = 1.0 + (x * (y / (1.0 + y)));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(1.0 - x)) / Float64(1.0 + y))
	tmp = 0.0
	if (t_0 <= 0.2)
		tmp = fma(Float64(1.0 - x), Float64(y / Float64(-1.0 - y)), 1.0);
	elseif (t_0 <= 500000000000.0)
		tmp = Float64(x - Float64(Float64(Float64(x + -1.0) + Float64(Float64(Float64(1.0 - x) - Float64(Float64(1.0 - x) / y)) / y)) / y));
	else
		tmp = Float64(1.0 + Float64(x * Float64(y / Float64(1.0 + y))));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.2], N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[t$95$0, 500000000000.0], N[(x - N[(N[(N[(x + -1.0), $MachinePrecision] + N[(N[(N[(1.0 - x), $MachinePrecision] - N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.20000000000000001

   1. Initial program 89.0%

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

      1. sub-neg 89.0%

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

      2. +-commutative 89.0%

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

      3. associate-/l* 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. fma-define 100.0%

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

      6. distribute-neg-frac2 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   if 0.20000000000000001 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 5e11

   1. Initial program 8.1%

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

      1. associate-/l* 8.1%

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

      2. remove-double-neg 8.1%

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

      3. remove-double-neg 8.1%

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

      4. +-commutative 8.1%

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

   3. Simplified 8.1%

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

   5. Taylor expanded in y around -inf 100.0%

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

   7. Simplified 100.0%

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

   if 5e11 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 61.4%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   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 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-neg-frac2 61.4%

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

      3. distribute-neg-in 61.4%

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

      4. metadata-eval 61.4%

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

      5. sub-neg 61.4%

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

      6. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{1 + y} \leq 0.2:\\ \;\;\;\;\mathsf{fma}\left(1 - x, \frac{y}{-1 - y}, 1\right)\\ \mathbf{elif}\;\frac{y \cdot \left(1 - x\right)}{1 + y} \leq 500000000000:\\ \;\;\;\;x - \frac{\left(x + -1\right) + \frac{\left(1 - x\right) - \frac{1 - x}{y}}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{y}{1 + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{1 + y}\\ \mathbf{if}\;t\_0 \leq 0.2:\\ \;\;\;\;1 + \frac{y}{-1 - y} \cdot \left(1 - x\right)\\ \mathbf{elif}\;t\_0 \leq 500000000000:\\ \;\;\;\;x - \frac{\left(x + -1\right) + \frac{\left(1 - x\right) - \frac{1 - x}{y}}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{y}{1 + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ 1.0 y))))
   (if (<= t_0 0.2)
     (+ 1.0 (* (/ y (- -1.0 y)) (- 1.0 x)))
     (if (<= t_0 500000000000.0)
       (- x (/ (+ (+ x -1.0) (/ (- (- 1.0 x) (/ (- 1.0 x) y)) y)) y))
       (+ 1.0 (* x (/ y (+ 1.0 y))))))))

C

double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (1.0 + y);
	double tmp;
	if (t_0 <= 0.2) {
		tmp = 1.0 + ((y / (-1.0 - y)) * (1.0 - x));
	} else if (t_0 <= 500000000000.0) {
		tmp = x - (((x + -1.0) + (((1.0 - x) - ((1.0 - x) / y)) / y)) / y);
	} else {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = (y * (1.0d0 - x)) / (1.0d0 + y)
    if (t_0 <= 0.2d0) then
        tmp = 1.0d0 + ((y / ((-1.0d0) - y)) * (1.0d0 - x))
    else if (t_0 <= 500000000000.0d0) then
        tmp = x - (((x + (-1.0d0)) + (((1.0d0 - x) - ((1.0d0 - x) / y)) / y)) / y)
    else
        tmp = 1.0d0 + (x * (y / (1.0d0 + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (1.0 + y);
	double tmp;
	if (t_0 <= 0.2) {
		tmp = 1.0 + ((y / (-1.0 - y)) * (1.0 - x));
	} else if (t_0 <= 500000000000.0) {
		tmp = x - (((x + -1.0) + (((1.0 - x) - ((1.0 - x) / y)) / y)) / y);
	} else {
		tmp = 1.0 + (x * (y / (1.0 + y)));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (1.0 - x)) / (1.0 + y)
	tmp = 0
	if t_0 <= 0.2:
		tmp = 1.0 + ((y / (-1.0 - y)) * (1.0 - x))
	elif t_0 <= 500000000000.0:
		tmp = x - (((x + -1.0) + (((1.0 - x) - ((1.0 - x) / y)) / y)) / y)
	else:
		tmp = 1.0 + (x * (y / (1.0 + y)))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(1.0 - x)) / Float64(1.0 + y))
	tmp = 0.0
	if (t_0 <= 0.2)
		tmp = Float64(1.0 + Float64(Float64(y / Float64(-1.0 - y)) * Float64(1.0 - x)));
	elseif (t_0 <= 500000000000.0)
		tmp = Float64(x - Float64(Float64(Float64(x + -1.0) + Float64(Float64(Float64(1.0 - x) - Float64(Float64(1.0 - x) / y)) / y)) / y));
	else
		tmp = Float64(1.0 + Float64(x * Float64(y / Float64(1.0 + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * (1.0 - x)) / (1.0 + y);
	tmp = 0.0;
	if (t_0 <= 0.2)
		tmp = 1.0 + ((y / (-1.0 - y)) * (1.0 - x));
	elseif (t_0 <= 500000000000.0)
		tmp = x - (((x + -1.0) + (((1.0 - x) - ((1.0 - x) / y)) / y)) / y);
	else
		tmp = 1.0 + (x * (y / (1.0 + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.2], N[(1.0 + N[(N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision] * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 500000000000.0], N[(x - N[(N[(N[(x + -1.0), $MachinePrecision] + N[(N[(N[(1.0 - x), $MachinePrecision] - N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.20000000000000001

   1. Initial program 89.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   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 0.20000000000000001 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 5e11

   1. Initial program 8.1%

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

      1. associate-/l* 8.1%

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

      2. remove-double-neg 8.1%

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

      3. remove-double-neg 8.1%

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

      4. +-commutative 8.1%

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

   3. Simplified 8.1%

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

   5. Taylor expanded in y around -inf 100.0%

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

   7. Simplified 100.0%

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

   if 5e11 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 61.4%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   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 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-neg-frac2 61.4%

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

      3. distribute-neg-in 61.4%

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

      4. metadata-eval 61.4%

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

      5. sub-neg 61.4%

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

      6. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{1 + y} \leq 0.2:\\ \;\;\;\;1 + \frac{y}{-1 - y} \cdot \left(1 - x\right)\\ \mathbf{elif}\;\frac{y \cdot \left(1 - x\right)}{1 + y} \leq 500000000000:\\ \;\;\;\;x - \frac{\left(x + -1\right) + \frac{\left(1 - x\right) - \frac{1 - x}{y}}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{y}{1 + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{1 + y}\\ \mathbf{if}\;t\_0 \leq 0.2:\\ \;\;\;\;1 + \frac{y}{-1 - y} \cdot \left(1 - x\right)\\ \mathbf{elif}\;t\_0 \leq 500000000000:\\ \;\;\;\;x + \frac{\left(1 - x\right) - \frac{1 - x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{y}{1 + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ 1.0 y))))
   (if (<= t_0 0.2)
     (+ 1.0 (* (/ y (- -1.0 y)) (- 1.0 x)))
     (if (<= t_0 500000000000.0)
       (+ x (/ (- (- 1.0 x) (/ (- 1.0 x) y)) y))
       (+ 1.0 (* x (/ y (+ 1.0 y))))))))

C

double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (1.0 + y);
	double tmp;
	if (t_0 <= 0.2) {
		tmp = 1.0 + ((y / (-1.0 - y)) * (1.0 - x));
	} else if (t_0 <= 500000000000.0) {
		tmp = x + (((1.0 - x) - ((1.0 - x) / y)) / y);
	} else {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = (y * (1.0d0 - x)) / (1.0d0 + y)
    if (t_0 <= 0.2d0) then
        tmp = 1.0d0 + ((y / ((-1.0d0) - y)) * (1.0d0 - x))
    else if (t_0 <= 500000000000.0d0) then
        tmp = x + (((1.0d0 - x) - ((1.0d0 - x) / y)) / y)
    else
        tmp = 1.0d0 + (x * (y / (1.0d0 + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (1.0 + y);
	double tmp;
	if (t_0 <= 0.2) {
		tmp = 1.0 + ((y / (-1.0 - y)) * (1.0 - x));
	} else if (t_0 <= 500000000000.0) {
		tmp = x + (((1.0 - x) - ((1.0 - x) / y)) / y);
	} else {
		tmp = 1.0 + (x * (y / (1.0 + y)));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (1.0 - x)) / (1.0 + y)
	tmp = 0
	if t_0 <= 0.2:
		tmp = 1.0 + ((y / (-1.0 - y)) * (1.0 - x))
	elif t_0 <= 500000000000.0:
		tmp = x + (((1.0 - x) - ((1.0 - x) / y)) / y)
	else:
		tmp = 1.0 + (x * (y / (1.0 + y)))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(1.0 - x)) / Float64(1.0 + y))
	tmp = 0.0
	if (t_0 <= 0.2)
		tmp = Float64(1.0 + Float64(Float64(y / Float64(-1.0 - y)) * Float64(1.0 - x)));
	elseif (t_0 <= 500000000000.0)
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) - Float64(Float64(1.0 - x) / y)) / y));
	else
		tmp = Float64(1.0 + Float64(x * Float64(y / Float64(1.0 + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * (1.0 - x)) / (1.0 + y);
	tmp = 0.0;
	if (t_0 <= 0.2)
		tmp = 1.0 + ((y / (-1.0 - y)) * (1.0 - x));
	elseif (t_0 <= 500000000000.0)
		tmp = x + (((1.0 - x) - ((1.0 - x) / y)) / y);
	else
		tmp = 1.0 + (x * (y / (1.0 + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.2], N[(1.0 + N[(N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision] * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 500000000000.0], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] - N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.20000000000000001

   1. Initial program 89.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   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 0.20000000000000001 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 5e11

   1. Initial program 8.1%

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

      1. associate-/l* 8.1%

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

      2. remove-double-neg 8.1%

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

      3. remove-double-neg 8.1%

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

      4. +-commutative 8.1%

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

   3. Simplified 8.1%

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

   5. Taylor expanded in y around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

      3. distribute-lft-out-- 99.8%

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

   7. Simplified 99.8%

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

   if 5e11 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 61.4%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   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 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-neg-frac2 61.4%

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

      3. distribute-neg-in 61.4%

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

      4. metadata-eval 61.4%

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

      5. sub-neg 61.4%

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

      6. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{1 + y} \leq 0.2:\\ \;\;\;\;1 + \frac{y}{-1 - y} \cdot \left(1 - x\right)\\ \mathbf{elif}\;\frac{y \cdot \left(1 - x\right)}{1 + y} \leq 500000000000:\\ \;\;\;\;x + \frac{\left(1 - x\right) - \frac{1 - x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{y}{1 + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{1 + y}\\ \mathbf{if}\;t\_0 \leq 1:\\ \;\;\;\;1 + \frac{y}{-1 - y} \cdot \left(1 - x\right)\\ \mathbf{elif}\;t\_0 \leq 500000000000:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{y}{1 + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ 1.0 y))))
   (if (<= t_0 1.0)
     (+ 1.0 (* (/ y (- -1.0 y)) (- 1.0 x)))
     (if (<= t_0 500000000000.0)
       (- x (/ -1.0 y))
       (+ 1.0 (* x (/ y (+ 1.0 y))))))))

C

double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (1.0 + y);
	double tmp;
	if (t_0 <= 1.0) {
		tmp = 1.0 + ((y / (-1.0 - y)) * (1.0 - x));
	} else if (t_0 <= 500000000000.0) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = (y * (1.0d0 - x)) / (1.0d0 + y)
    if (t_0 <= 1.0d0) then
        tmp = 1.0d0 + ((y / ((-1.0d0) - y)) * (1.0d0 - x))
    else if (t_0 <= 500000000000.0d0) then
        tmp = x - ((-1.0d0) / y)
    else
        tmp = 1.0d0 + (x * (y / (1.0d0 + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (1.0 + y);
	double tmp;
	if (t_0 <= 1.0) {
		tmp = 1.0 + ((y / (-1.0 - y)) * (1.0 - x));
	} else if (t_0 <= 500000000000.0) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 1.0 + (x * (y / (1.0 + y)));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (1.0 - x)) / (1.0 + y)
	tmp = 0
	if t_0 <= 1.0:
		tmp = 1.0 + ((y / (-1.0 - y)) * (1.0 - x))
	elif t_0 <= 500000000000.0:
		tmp = x - (-1.0 / y)
	else:
		tmp = 1.0 + (x * (y / (1.0 + y)))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(1.0 - x)) / Float64(1.0 + y))
	tmp = 0.0
	if (t_0 <= 1.0)
		tmp = Float64(1.0 + Float64(Float64(y / Float64(-1.0 - y)) * Float64(1.0 - x)));
	elseif (t_0 <= 500000000000.0)
		tmp = Float64(x - Float64(-1.0 / y));
	else
		tmp = Float64(1.0 + Float64(x * Float64(y / Float64(1.0 + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * (1.0 - x)) / (1.0 + y);
	tmp = 0.0;
	if (t_0 <= 1.0)
		tmp = 1.0 + ((y / (-1.0 - y)) * (1.0 - x));
	elseif (t_0 <= 500000000000.0)
		tmp = x - (-1.0 / y);
	else
		tmp = 1.0 + (x * (y / (1.0 + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 1.0], N[(1.0 + N[(N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision] * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 500000000000.0], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 59.9%

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

      1. associate-/l* 67.1%

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

      2. remove-double-neg 67.1%

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

      3. remove-double-neg 67.1%

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

      4. +-commutative 67.1%

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

   3. Simplified 67.1%

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

   if 1 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 5e11

   1. Initial program 73.7%

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

      1. associate-/l* 73.7%

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

      2. remove-double-neg 73.7%

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

      3. remove-double-neg 73.7%

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

      4. +-commutative 73.7%

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

   3. Simplified 73.7%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. neg-sub0 100.0%

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

      6. +-commutative 100.0%

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

      7. sub-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

   if 5e11 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 61.4%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   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 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-neg-frac2 61.4%

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

      3. distribute-neg-in 61.4%

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

      4. metadata-eval 61.4%

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

      5. sub-neg 61.4%

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

      6. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{1 + y} \leq 1:\\ \;\;\;\;1 + \frac{y}{-1 - y} \cdot \left(1 - x\right)\\ \mathbf{elif}\;\frac{y \cdot \left(1 - x\right)}{1 + y} \leq 500000000000:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{y}{1 + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-81}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y 5.5e-81)
     1.0
     (if (<= y 1.7e-7) (* x y) (if (<= y 3.5e+70) (/ 1.0 y) x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 5.5e-81) {
		tmp = 1.0;
	} else if (y <= 1.7e-7) {
		tmp = x * y;
	} else if (y <= 3.5e+70) {
		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 <= 5.5d-81) then
        tmp = 1.0d0
    else if (y <= 1.7d-7) then
        tmp = x * y
    else if (y <= 3.5d+70) 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 <= 5.5e-81) {
		tmp = 1.0;
	} else if (y <= 1.7e-7) {
		tmp = x * y;
	} else if (y <= 3.5e+70) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 5.5e-81:
		tmp = 1.0
	elif y <= 1.7e-7:
		tmp = x * y
	elif y <= 3.5e+70:
		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 <= 5.5e-81)
		tmp = 1.0;
	elseif (y <= 1.7e-7)
		tmp = Float64(x * y);
	elseif (y <= 3.5e+70)
		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 <= 5.5e-81)
		tmp = 1.0;
	elseif (y <= 1.7e-7)
		tmp = x * y;
	elseif (y <= 3.5e+70)
		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, 5.5e-81], 1.0, If[LessEqual[y, 1.7e-7], N[(x * y), $MachinePrecision], If[LessEqual[y, 3.5e+70], N[(1.0 / y), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1 or 3.50000000000000002e70 < y

   1. Initial program 27.0%

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

      1. associate-/l* 53.5%

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

      2. remove-double-neg 53.5%

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

      3. remove-double-neg 53.5%

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

      4. +-commutative 53.5%

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

   3. Simplified 53.5%

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

   5. Taylor expanded in y around inf 78.2%

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

   if -1 < y < 5.50000000000000026e-81

   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 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-neg-frac2 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. sub-neg 100.0%

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

      6. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 80.9%

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

   if 5.50000000000000026e-81 < y < 1.69999999999999987e-7

   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 99.4%

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

      1. mul-1-neg 99.4%

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

      2. distribute-neg-frac2 99.4%

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

      3. distribute-neg-in 99.4%

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

      4. metadata-eval 99.4%

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

      5. sub-neg 99.4%

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

      6. associate-*r/ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in x around inf 62.8%

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

      1. +-commutative 62.8%

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

   10. Simplified 62.8%

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

   11. Taylor expanded in y around 0 61.9%

       \[\leadsto \color{blue}{x \cdot y} \]
   12. Step-by-step derivation

       1. *-commutative 61.9%

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

   13. Simplified 61.9%

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

   if 1.69999999999999987e-7 < y < 3.50000000000000002e70

   1. Initial program 26.9%

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

      1. associate-/l* 27.0%

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

      2. remove-double-neg 27.0%

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

      3. remove-double-neg 27.0%

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

      4. +-commutative 27.0%

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

   3. Simplified 27.0%

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

   5. Taylor expanded in y around -inf 91.6%

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

      1. associate-*r/ 91.6%

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

      2. mul-1-neg 91.6%

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

      3. neg-sub0 91.6%

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

      4. associate-+l- 91.6%

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

      5. neg-sub0 91.6%

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

      6. +-commutative 91.6%

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

      7. sub-neg 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in x around 0 61.4%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-81}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{-1}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-81}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- x (/ -1.0 y))))
   (if (<= y -1.0)
     t_0
     (if (<= y 5.8e-81) 1.0 (if (<= y 1.7e-7) (* x y) t_0)))))

C

double code(double x, double y) {
	double t_0 = x - (-1.0 / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 5.8e-81) {
		tmp = 1.0;
	} else if (y <= 1.7e-7) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x - ((-1.0d0) / y)
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 5.8d-81) then
        tmp = 1.0d0
    else if (y <= 1.7d-7) then
        tmp = x * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x - (-1.0 / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 5.8e-81) {
		tmp = 1.0;
	} else if (y <= 1.7e-7) {
		tmp = x * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x - (-1.0 / y)
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 5.8e-81:
		tmp = 1.0
	elif y <= 1.7e-7:
		tmp = x * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x - Float64(-1.0 / y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 5.8e-81)
		tmp = 1.0;
	elseif (y <= 1.7e-7)
		tmp = Float64(x * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x - (-1.0 / y);
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 5.8e-81)
		tmp = 1.0;
	elseif (y <= 1.7e-7)
		tmp = x * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 5.8e-81], 1.0, If[LessEqual[y, 1.7e-7], N[(x * y), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1.69999999999999987e-7 < y

   1. Initial program 27.0%

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

      1. associate-/l* 50.4%

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

      2. remove-double-neg 50.4%

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

      3. remove-double-neg 50.4%

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

      4. +-commutative 50.4%

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

   3. Simplified 50.4%

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

   5. Taylor expanded in y around -inf 99.0%

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

      1. associate-*r/ 99.0%

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

      2. mul-1-neg 99.0%

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

      3. neg-sub0 99.0%

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

      4. associate-+l- 99.0%

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

      5. neg-sub0 99.0%

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

      6. +-commutative 99.0%

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

      7. sub-neg 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in x around 0 99.0%

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

   if -1 < y < 5.79999999999999978e-81

   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 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-neg-frac2 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. sub-neg 100.0%

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

      6. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 80.9%

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

   if 5.79999999999999978e-81 < y < 1.69999999999999987e-7

   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 99.4%

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

      1. mul-1-neg 99.4%

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

      2. distribute-neg-frac2 99.4%

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

      3. distribute-neg-in 99.4%

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

      4. metadata-eval 99.4%

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

      5. sub-neg 99.4%

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

      6. associate-*r/ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in x around inf 62.8%

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

      1. +-commutative 62.8%

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

   10. Simplified 62.8%

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

   11. Taylor expanded in y around 0 61.9%

       \[\leadsto \color{blue}{x \cdot y} \]
   12. Step-by-step derivation

       1. *-commutative 61.9%

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

   13. Simplified 61.9%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-81}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-81}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 4.1e-81) 1.0 (if (<= y 1.7e-7) (* x y) x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 4.1e-81) {
		tmp = 1.0;
	} else if (y <= 1.7e-7) {
		tmp = x * 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 <= 4.1d-81) then
        tmp = 1.0d0
    else if (y <= 1.7d-7) then
        tmp = x * 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 <= 4.1e-81) {
		tmp = 1.0;
	} else if (y <= 1.7e-7) {
		tmp = x * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 4.1e-81:
		tmp = 1.0
	elif y <= 1.7e-7:
		tmp = x * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 4.1e-81)
		tmp = 1.0;
	elseif (y <= 1.7e-7)
		tmp = Float64(x * 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 <= 4.1e-81)
		tmp = 1.0;
	elseif (y <= 1.7e-7)
		tmp = x * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 4.1e-81], 1.0, If[LessEqual[y, 1.7e-7], N[(x * y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1.69999999999999987e-7 < y

   1. Initial program 27.0%

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

      1. associate-/l* 50.4%

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

      2. remove-double-neg 50.4%

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

      3. remove-double-neg 50.4%

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

      4. +-commutative 50.4%

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

   3. Simplified 50.4%

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

   5. Taylor expanded in y around inf 73.0%

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

   if -1 < y < 4.09999999999999984e-81

   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 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-neg-frac2 100.0%

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

      3. distribute-neg-in 100.0%

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

      4. metadata-eval 100.0%

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

      5. sub-neg 100.0%

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

      6. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 80.9%

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

   if 4.09999999999999984e-81 < y < 1.69999999999999987e-7

   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 99.4%

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

      1. mul-1-neg 99.4%

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

      2. distribute-neg-frac2 99.4%

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

      3. distribute-neg-in 99.4%

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

      4. metadata-eval 99.4%

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

      5. sub-neg 99.4%

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

      6. associate-*r/ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in x around inf 62.8%

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

      1. +-commutative 62.8%

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

   10. Simplified 62.8%

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

   11. Taylor expanded in y around 0 61.9%

       \[\leadsto \color{blue}{x \cdot y} \]
   12. Step-by-step derivation

       1. *-commutative 61.9%

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

   13. Simplified 61.9%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-81}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.82\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.82)))
   (- x (/ -1.0 y))
   (- 1.0 (* y (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.82)) {
		tmp = x - (-1.0 / 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 <= 0.82d0))) then
        tmp = x - ((-1.0d0) / 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 <= 0.82)) {
		tmp = x - (-1.0 / 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 <= 0.82):
		tmp = x - (-1.0 / y)
	else:
		tmp = 1.0 - (y * (1.0 - x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.82))
		tmp = Float64(x - Float64(-1.0 / 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 <= 0.82)))
		tmp = x - (-1.0 / 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, 0.82]], $MachinePrecision]], N[(x - N[(-1.0 / 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 0.819999999999999951 < y

   1. Initial program 26.5%

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

      1. associate-/l* 50.1%

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

      2. remove-double-neg 50.1%

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

      3. remove-double-neg 50.1%

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

      4. +-commutative 50.1%

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

   3. Simplified 50.1%

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

   5. Taylor expanded in y around -inf 99.7%

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

      1. associate-*r/ 99.7%

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

      2. mul-1-neg 99.7%

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

      3. neg-sub0 99.7%

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

      4. associate-+l- 99.7%

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

      5. neg-sub0 99.7%

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

      6. +-commutative 99.7%

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

      7. sub-neg 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around 0 99.7%

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

   if -1 < y < 0.819999999999999951

   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 99.7%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.82\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 26.5%

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

      1. associate-/l* 50.1%

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

      2. remove-double-neg 50.1%

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

      3. remove-double-neg 50.1%

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

      4. +-commutative 50.1%

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

   3. Simplified 50.1%

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

   5. Taylor expanded in y around -inf 99.7%

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

      1. associate-*r/ 99.7%

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

      2. mul-1-neg 99.7%

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

      3. neg-sub0 99.7%

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

      4. associate-+l- 99.7%

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

      5. neg-sub0 99.7%

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

      6. +-commutative 99.7%

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

      7. sub-neg 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around 0 99.7%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. 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 99.5%

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

      1. mul-1-neg 99.5%

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

      2. distribute-neg-frac2 99.5%

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

      3. distribute-neg-in 99.5%

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

      4. metadata-eval 99.5%

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

      5. sub-neg 99.5%

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

      6. associate-*r/ 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in y around 0 99.3%

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

      1. +-commutative 99.3%

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

   10. Simplified 99.3%

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

4. Final simplification 99.5%

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

Alternative 10: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6600000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 6600000.0) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 6600000.0) {
		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 <= 6600000.0d0) 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 <= 6600000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 6600000.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 6600000.0)
		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 <= 6600000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 6600000.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 6.6e6 < y

   1. Initial program 26.2%

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

      1. associate-/l* 49.9%

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

      2. remove-double-neg 49.9%

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

      3. remove-double-neg 49.9%

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

      4. +-commutative 49.9%

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

   3. Simplified 49.9%

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

   5. Taylor expanded in y around inf 74.0%

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

   if -1 < y < 6.6e6

   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 x around inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. distribute-neg-frac2 98.7%

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

      3. distribute-neg-in 98.7%

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

      4. metadata-eval 98.7%

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

      5. sub-neg 98.7%

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

      6. associate-*r/ 98.7%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in x around 0 72.6%

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

Alternative 11: 39.0% 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 60.4%

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

   1. associate-/l* 73.1%

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

   2. remove-double-neg 73.1%

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

   3. remove-double-neg 73.1%

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

   4. +-commutative 73.1%

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

3. Simplified 73.1%

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

5. Taylor expanded in x around inf 59.2%

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

   1. mul-1-neg 59.2%

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

   2. distribute-neg-frac2 59.2%

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

   3. distribute-neg-in 59.2%

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

   4. metadata-eval 59.2%

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

   5. sub-neg 59.2%

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

   6. associate-*r/ 71.9%

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

7. Simplified 71.9%

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

8. Taylor expanded in x around 0 35.7%

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

Developer Target 1: 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 2024150 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -36938482788297247/10000000000000) (- (/ 1 y) (- (/ x y) x)) (if (< y 679931050341891/100000) (- 1 (/ (* (- 1 x) y) (+ y 1))) (- (/ 1 y) (- (/ x y) x)))))

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