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

Percentage Accurate: 65.3% → 99.9%

Time: 13.3s

Alternatives: 13

Speedup: 2.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 65.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1 - x}{y}\\ t_1 := \frac{x + -1}{{y}^{2}}\\ \mathbf{if}\;y \leq -290000:\\ \;\;\;\;\left(x + t_0\right) + t_1\\ \mathbf{elif}\;y \leq 11800:\\ \;\;\;\;\mathsf{fma}\left(\frac{x + -1}{y + 1}, y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_1 + \left(\frac{1 - x}{{y}^{3}} + t_0\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- 1.0 x) y)) (t_1 (/ (+ x -1.0) (pow y 2.0))))
   (if (<= y -290000.0)
     (+ (+ x t_0) t_1)
     (if (<= y 11800.0)
       (fma (/ (+ x -1.0) (+ y 1.0)) y 1.0)
       (+ x (+ t_1 (+ (/ (- 1.0 x) (pow y 3.0)) t_0)))))))

C

double code(double x, double y) {
	double t_0 = (1.0 - x) / y;
	double t_1 = (x + -1.0) / pow(y, 2.0);
	double tmp;
	if (y <= -290000.0) {
		tmp = (x + t_0) + t_1;
	} else if (y <= 11800.0) {
		tmp = fma(((x + -1.0) / (y + 1.0)), y, 1.0);
	} else {
		tmp = x + (t_1 + (((1.0 - x) / pow(y, 3.0)) + t_0));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 - x) / y)
	t_1 = Float64(Float64(x + -1.0) / (y ^ 2.0))
	tmp = 0.0
	if (y <= -290000.0)
		tmp = Float64(Float64(x + t_0) + t_1);
	elseif (y <= 11800.0)
		tmp = fma(Float64(Float64(x + -1.0) / Float64(y + 1.0)), y, 1.0);
	else
		tmp = Float64(x + Float64(t_1 + Float64(Float64(Float64(1.0 - x) / (y ^ 3.0)) + t_0)));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + -1.0), $MachinePrecision] / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -290000.0], N[(N[(x + t$95$0), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[y, 11800.0], N[(N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * y + 1.0), $MachinePrecision], N[(x + N[(t$95$1 + N[(N[(N[(1.0 - x), $MachinePrecision] / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9e5

   1. Initial program 31.8%

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

      1. associate-*l/ 47.4%

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

      2. +-commutative 47.4%

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

   3. Simplified 47.4%

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

   4. Taylor expanded in y around -inf 100.0%

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

      1. associate-+r+ 100.0%

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

      2. associate--l+ 100.0%

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

      3. mul-1-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. div-sub 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

   if -2.9e5 < y < 11800

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-*l/ 99.9%

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

      4. distribute-lft-neg-in 99.9%

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

      5. fma-def 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. neg-sub0 99.9%

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

      8. associate--r- 99.9%

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

      9. metadata-eval 99.9%

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

      10. +-commutative 99.9%

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

      11. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   if 11800 < y

   1. Initial program 34.0%

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

      1. associate-*l/ 60.0%

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

      2. +-commutative 60.0%

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

   3. Simplified 60.0%

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

   4. Taylor expanded in y around -inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-+r+ 99.7%

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

      3. associate--l+ 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -290000:\\ \;\;\;\;\left(x + \frac{1 - x}{y}\right) + \frac{x + -1}{{y}^{2}}\\ \mathbf{elif}\;y \leq 11800:\\ \;\;\;\;\mathsf{fma}\left(\frac{x + -1}{y + 1}, y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{x + -1}{{y}^{2}} + \left(\frac{1 - x}{{y}^{3}} + \frac{1 - x}{y}\right)\right)\\ \end{array} \]

Alternative 2: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -23000000 \lor \neg \left(y \leq 320000\right):\\ \;\;\;\;\left(x + \frac{1 - x}{y}\right) + \frac{x + -1}{{y}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \left(x + -1\right)}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -23000000.0) (not (<= y 320000.0)))
   (+ (+ x (/ (- 1.0 x) y)) (/ (+ x -1.0) (pow y 2.0)))
   (+ 1.0 (/ (* y (+ x -1.0)) (+ y 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -23000000.0) || !(y <= 320000.0)) {
		tmp = (x + ((1.0 - x) / y)) + ((x + -1.0) / pow(y, 2.0));
	} else {
		tmp = 1.0 + ((y * (x + -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 <= (-23000000.0d0)) .or. (.not. (y <= 320000.0d0))) then
        tmp = (x + ((1.0d0 - x) / y)) + ((x + (-1.0d0)) / (y ** 2.0d0))
    else
        tmp = 1.0d0 + ((y * (x + (-1.0d0))) / (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -23000000.0) || !(y <= 320000.0)) {
		tmp = (x + ((1.0 - x) / y)) + ((x + -1.0) / Math.pow(y, 2.0));
	} else {
		tmp = 1.0 + ((y * (x + -1.0)) / (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -23000000.0) or not (y <= 320000.0):
		tmp = (x + ((1.0 - x) / y)) + ((x + -1.0) / math.pow(y, 2.0))
	else:
		tmp = 1.0 + ((y * (x + -1.0)) / (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -23000000.0) || !(y <= 320000.0))
		tmp = Float64(Float64(x + Float64(Float64(1.0 - x) / y)) + Float64(Float64(x + -1.0) / (y ^ 2.0)));
	else
		tmp = Float64(1.0 + Float64(Float64(y * Float64(x + -1.0)) / Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -23000000.0) || ~((y <= 320000.0)))
		tmp = (x + ((1.0 - x) / y)) + ((x + -1.0) / (y ^ 2.0));
	else
		tmp = 1.0 + ((y * (x + -1.0)) / (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -23000000.0], N[Not[LessEqual[y, 320000.0]], $MachinePrecision]], N[(N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e7 or 3.2e5 < y

   1. Initial program 31.3%

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

      1. associate-*l/ 52.5%

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

      2. +-commutative 52.5%

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

   3. Simplified 52.5%

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

   4. Taylor expanded in y around -inf 99.9%

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

      1. associate-+r+ 99.9%

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

      2. associate--l+ 99.9%

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

      3. mul-1-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

      7. div-sub 99.9%

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

      8. sub-neg 99.9%

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

      9. metadata-eval 99.9%

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

   6. Simplified 99.9%

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

   if -2.3e7 < y < 3.2e5

   1. Initial program 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -23000000 \lor \neg \left(y \leq 320000\right):\\ \;\;\;\;\left(x + \frac{1 - x}{y}\right) + \frac{x + -1}{{y}^{2}}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \left(x + -1\right)}{y + 1}\\ \end{array} \]

Alternative 3: 70.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -90:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-104}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-123}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.86 \cdot 10^{-50}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+125}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -90.0)
   x
   (if (<= y -4e-104)
     (* y x)
     (if (<= y 6.2e-123)
       1.0
       (if (<= y 1.86e-50)
         (* y x)
         (if (<= y 5.5e-5)
           (- 1.0 y)
           (if (<= y 6.1e+94) x (if (<= y 9.2e+125) (/ 1.0 y) x))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -90.0) {
		tmp = x;
	} else if (y <= -4e-104) {
		tmp = y * x;
	} else if (y <= 6.2e-123) {
		tmp = 1.0;
	} else if (y <= 1.86e-50) {
		tmp = y * x;
	} else if (y <= 5.5e-5) {
		tmp = 1.0 - y;
	} else if (y <= 6.1e+94) {
		tmp = x;
	} else if (y <= 9.2e+125) {
		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 <= (-90.0d0)) then
        tmp = x
    else if (y <= (-4d-104)) then
        tmp = y * x
    else if (y <= 6.2d-123) then
        tmp = 1.0d0
    else if (y <= 1.86d-50) then
        tmp = y * x
    else if (y <= 5.5d-5) then
        tmp = 1.0d0 - y
    else if (y <= 6.1d+94) then
        tmp = x
    else if (y <= 9.2d+125) 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 <= -90.0) {
		tmp = x;
	} else if (y <= -4e-104) {
		tmp = y * x;
	} else if (y <= 6.2e-123) {
		tmp = 1.0;
	} else if (y <= 1.86e-50) {
		tmp = y * x;
	} else if (y <= 5.5e-5) {
		tmp = 1.0 - y;
	} else if (y <= 6.1e+94) {
		tmp = x;
	} else if (y <= 9.2e+125) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -90.0:
		tmp = x
	elif y <= -4e-104:
		tmp = y * x
	elif y <= 6.2e-123:
		tmp = 1.0
	elif y <= 1.86e-50:
		tmp = y * x
	elif y <= 5.5e-5:
		tmp = 1.0 - y
	elif y <= 6.1e+94:
		tmp = x
	elif y <= 9.2e+125:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -90.0)
		tmp = x;
	elseif (y <= -4e-104)
		tmp = Float64(y * x);
	elseif (y <= 6.2e-123)
		tmp = 1.0;
	elseif (y <= 1.86e-50)
		tmp = Float64(y * x);
	elseif (y <= 5.5e-5)
		tmp = Float64(1.0 - y);
	elseif (y <= 6.1e+94)
		tmp = x;
	elseif (y <= 9.2e+125)
		tmp = Float64(1.0 / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -90.0)
		tmp = x;
	elseif (y <= -4e-104)
		tmp = y * x;
	elseif (y <= 6.2e-123)
		tmp = 1.0;
	elseif (y <= 1.86e-50)
		tmp = y * x;
	elseif (y <= 5.5e-5)
		tmp = 1.0 - y;
	elseif (y <= 6.1e+94)
		tmp = x;
	elseif (y <= 9.2e+125)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -90.0], x, If[LessEqual[y, -4e-104], N[(y * x), $MachinePrecision], If[LessEqual[y, 6.2e-123], 1.0, If[LessEqual[y, 1.86e-50], N[(y * x), $MachinePrecision], If[LessEqual[y, 5.5e-5], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, 6.1e+94], x, If[LessEqual[y, 9.2e+125], N[(1.0 / y), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -90 or 5.5000000000000002e-5 < y < 6.10000000000000035e94 or 9.20000000000000051e125 < y

   1. Initial program 35.6%

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

      1. associate-*l/ 57.0%

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

      2. +-commutative 57.0%

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

   3. Simplified 57.0%

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

   4. Taylor expanded in y around inf 70.5%

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

   if -90 < y < -3.99999999999999971e-104 or 6.19999999999999996e-123 < y < 1.86000000000000007e-50

   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%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 61.1%

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

      1. /-rgt-identity 61.1%

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

      2. associate-/r/ 60.9%

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

      3. associate-/r* 60.9%

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

      4. +-commutative 60.9%

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

      5. distribute-lft-in 60.9%

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

      6. lft-mult-inverse 60.9%

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

      7. *-rgt-identity 60.9%

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

   6. Simplified 60.9%

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

   7. Taylor expanded in y around 0 58.5%

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

      1. *-commutative 58.5%

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

   9. Simplified 58.5%

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

   if -3.99999999999999971e-104 < y < 6.19999999999999996e-123

   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%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 90.6%

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

   if 1.86000000000000007e-50 < y < 5.5000000000000002e-5

   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%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 68.9%

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

   5. Taylor expanded in y around 0 68.9%

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

      1. neg-mul-1 68.9%

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

      2. unsub-neg 68.9%

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

   7. Simplified 68.9%

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

   if 6.10000000000000035e94 < y < 9.20000000000000051e125

   1. Initial program 16.1%

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

      1. associate-*l/ 16.3%

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

      2. +-commutative 16.3%

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

   3. Simplified 16.3%

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

   4. Taylor expanded in y around -inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in x around 0 74.9%

      \[\leadsto \color{blue}{\frac{1}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -90:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-104}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-123}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.86 \cdot 10^{-50}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+125}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 70.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{x}{y}\\ \mathbf{if}\;y \leq -90:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-104}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-123}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-50}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+97}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+125}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- x (/ x y))))
   (if (<= y -90.0)
     t_0
     (if (<= y -4e-104)
       (* y x)
       (if (<= y 2.75e-123)
         1.0
         (if (<= y 2.1e-50)
           (* y x)
           (if (<= y 1.0)
             (- 1.0 y)
             (if (<= y 1.8e+97) t_0 (if (<= y 9e+125) (/ 1.0 y) x)))))))))

C

double code(double x, double y) {
	double t_0 = x - (x / y);
	double tmp;
	if (y <= -90.0) {
		tmp = t_0;
	} else if (y <= -4e-104) {
		tmp = y * x;
	} else if (y <= 2.75e-123) {
		tmp = 1.0;
	} else if (y <= 2.1e-50) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = 1.0 - y;
	} else if (y <= 1.8e+97) {
		tmp = t_0;
	} else if (y <= 9e+125) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x - (x / y)
    if (y <= (-90.0d0)) then
        tmp = t_0
    else if (y <= (-4d-104)) then
        tmp = y * x
    else if (y <= 2.75d-123) then
        tmp = 1.0d0
    else if (y <= 2.1d-50) then
        tmp = y * x
    else if (y <= 1.0d0) then
        tmp = 1.0d0 - y
    else if (y <= 1.8d+97) then
        tmp = t_0
    else if (y <= 9d+125) then
        tmp = 1.0d0 / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x - (x / y);
	double tmp;
	if (y <= -90.0) {
		tmp = t_0;
	} else if (y <= -4e-104) {
		tmp = y * x;
	} else if (y <= 2.75e-123) {
		tmp = 1.0;
	} else if (y <= 2.1e-50) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = 1.0 - y;
	} else if (y <= 1.8e+97) {
		tmp = t_0;
	} else if (y <= 9e+125) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x - (x / y)
	tmp = 0
	if y <= -90.0:
		tmp = t_0
	elif y <= -4e-104:
		tmp = y * x
	elif y <= 2.75e-123:
		tmp = 1.0
	elif y <= 2.1e-50:
		tmp = y * x
	elif y <= 1.0:
		tmp = 1.0 - y
	elif y <= 1.8e+97:
		tmp = t_0
	elif y <= 9e+125:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x - Float64(x / y))
	tmp = 0.0
	if (y <= -90.0)
		tmp = t_0;
	elseif (y <= -4e-104)
		tmp = Float64(y * x);
	elseif (y <= 2.75e-123)
		tmp = 1.0;
	elseif (y <= 2.1e-50)
		tmp = Float64(y * x);
	elseif (y <= 1.0)
		tmp = Float64(1.0 - y);
	elseif (y <= 1.8e+97)
		tmp = t_0;
	elseif (y <= 9e+125)
		tmp = Float64(1.0 / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x - (x / y);
	tmp = 0.0;
	if (y <= -90.0)
		tmp = t_0;
	elseif (y <= -4e-104)
		tmp = y * x;
	elseif (y <= 2.75e-123)
		tmp = 1.0;
	elseif (y <= 2.1e-50)
		tmp = y * x;
	elseif (y <= 1.0)
		tmp = 1.0 - y;
	elseif (y <= 1.8e+97)
		tmp = t_0;
	elseif (y <= 9e+125)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -90.0], t$95$0, If[LessEqual[y, -4e-104], N[(y * x), $MachinePrecision], If[LessEqual[y, 2.75e-123], 1.0, If[LessEqual[y, 2.1e-50], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.0], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, 1.8e+97], t$95$0, If[LessEqual[y, 9e+125], N[(1.0 / y), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -90 or 1 < y < 1.79999999999999983e97

   1. Initial program 38.2%

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

      1. associate-*l/ 52.8%

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

      2. +-commutative 52.8%

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

   3. Simplified 52.8%

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

   4. Taylor expanded in x around inf 56.8%

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

      1. /-rgt-identity 56.8%

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

      2. associate-/r/ 56.6%

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

      3. associate-/r* 71.4%

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

      4. +-commutative 71.4%

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

      5. distribute-lft-in 71.5%

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

      6. lft-mult-inverse 71.6%

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

      7. *-rgt-identity 71.6%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in y around inf 70.4%

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

      1. mul-1-neg 70.4%

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

      2. unsub-neg 70.4%

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

   9. Simplified 70.4%

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

   if -90 < y < -3.99999999999999971e-104 or 2.75e-123 < y < 2.1000000000000001e-50

   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%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 61.1%

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

      1. /-rgt-identity 61.1%

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

      2. associate-/r/ 60.9%

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

      3. associate-/r* 60.9%

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

      4. +-commutative 60.9%

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

      5. distribute-lft-in 60.9%

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

      6. lft-mult-inverse 60.9%

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

      7. *-rgt-identity 60.9%

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

   6. Simplified 60.9%

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

   7. Taylor expanded in y around 0 58.5%

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

      1. *-commutative 58.5%

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

   9. Simplified 58.5%

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

   if -3.99999999999999971e-104 < y < 2.75e-123

   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%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 90.6%

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

   if 2.1000000000000001e-50 < y < 1

   1. Initial program 99.6%

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

      1. associate-*l/ 99.7%

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

      2. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 57.3%

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

   5. Taylor expanded in y around 0 57.3%

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

      1. neg-mul-1 57.3%

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

      2. unsub-neg 57.3%

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

   7. Simplified 57.3%

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

   if 1.79999999999999983e97 < y < 9.0000000000000001e125

   1. Initial program 16.1%

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

      1. associate-*l/ 16.3%

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

      2. +-commutative 16.3%

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

   3. Simplified 16.3%

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

   4. Taylor expanded in y around -inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in x around 0 74.9%

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

   if 9.0000000000000001e125 < y

   1. Initial program 24.1%

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

      1. associate-*l/ 66.3%

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

      2. +-commutative 66.3%

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

   3. Simplified 66.3%

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

   4. Taylor expanded in y around inf 78.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -90:\\ \;\;\;\;x - \frac{x}{y}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-104}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-123}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-50}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+97}:\\ \;\;\;\;x - \frac{x}{y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+125}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -110000000 \lor \neg \left(y \leq 230000000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -110000000.0) (not (<= y 230000000.0)))
   (+ x (/ (- 1.0 x) y))
   (+ 1.0 (* y (/ (+ x -1.0) (+ y 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -110000000.0) || !(y <= 230000000.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + (y * ((x + -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 <= (-110000000.0d0)) .or. (.not. (y <= 230000000.0d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 + (y * ((x + (-1.0d0)) / (y + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -110000000.0) || !(y <= 230000000.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -110000000.0) or not (y <= 230000000.0):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -110000000.0) || !(y <= 230000000.0))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(1.0 + Float64(y * Float64(Float64(x + -1.0) / Float64(y + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -110000000.0) || ~((y <= 230000000.0)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -110000000.0], N[Not[LessEqual[y, 230000000.0]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e8 or 2.3e8 < y

   1. Initial program 30.5%

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

      1. associate-*l/ 51.9%

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

      2. +-commutative 51.9%

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

   3. Simplified 51.9%

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

   4. Taylor expanded in y around -inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

      3. sub-neg 99.5%

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

      4. metadata-eval 99.5%

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

   6. Simplified 99.5%

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

   if -1.1e8 < y < 2.3e8

   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%

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

      2. +-commutative 99.5%

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

   3. Simplified 99.5%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -110000000 \lor \neg \left(y \leq 230000000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \end{array} \]

Alternative 6: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -180000000 \lor \neg \left(y \leq 155000000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \left(x + -1\right)}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -180000000.0) (not (<= y 155000000.0)))
   (+ x (/ (- 1.0 x) y))
   (+ 1.0 (/ (* y (+ x -1.0)) (+ y 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -180000000.0) || !(y <= 155000000.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + ((y * (x + -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 <= (-180000000.0d0)) .or. (.not. (y <= 155000000.0d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 + ((y * (x + (-1.0d0))) / (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -180000000.0) || !(y <= 155000000.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + ((y * (x + -1.0)) / (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -180000000.0) or not (y <= 155000000.0):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 + ((y * (x + -1.0)) / (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -180000000.0) || !(y <= 155000000.0))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(1.0 + Float64(Float64(y * Float64(x + -1.0)) / Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -180000000.0) || ~((y <= 155000000.0)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = 1.0 + ((y * (x + -1.0)) / (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -180000000.0], N[Not[LessEqual[y, 155000000.0]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e8 or 1.55e8 < y

   1. Initial program 30.5%

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

      1. associate-*l/ 51.9%

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

      2. +-commutative 51.9%

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

   3. Simplified 51.9%

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

   4. Taylor expanded in y around -inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

      3. sub-neg 99.5%

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

      4. metadata-eval 99.5%

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

   6. Simplified 99.5%

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

   if -1.8e8 < y < 1.55e8

   1. Initial program 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -180000000 \lor \neg \left(y \leq 155000000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \left(x + -1\right)}{y + 1}\\ \end{array} \]

Alternative 7: 71.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -90:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-105}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-123}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-50}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -90.0)
   x
   (if (<= y -5.8e-105)
     (* y x)
     (if (<= y 6.2e-123)
       1.0
       (if (<= y 1.15e-50) (* y x) (if (<= y 5.5e-5) (- 1.0 y) x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -90.0) {
		tmp = x;
	} else if (y <= -5.8e-105) {
		tmp = y * x;
	} else if (y <= 6.2e-123) {
		tmp = 1.0;
	} else if (y <= 1.15e-50) {
		tmp = y * x;
	} else if (y <= 5.5e-5) {
		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 <= (-90.0d0)) then
        tmp = x
    else if (y <= (-5.8d-105)) then
        tmp = y * x
    else if (y <= 6.2d-123) then
        tmp = 1.0d0
    else if (y <= 1.15d-50) then
        tmp = y * x
    else if (y <= 5.5d-5) 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 <= -90.0) {
		tmp = x;
	} else if (y <= -5.8e-105) {
		tmp = y * x;
	} else if (y <= 6.2e-123) {
		tmp = 1.0;
	} else if (y <= 1.15e-50) {
		tmp = y * x;
	} else if (y <= 5.5e-5) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -90.0:
		tmp = x
	elif y <= -5.8e-105:
		tmp = y * x
	elif y <= 6.2e-123:
		tmp = 1.0
	elif y <= 1.15e-50:
		tmp = y * x
	elif y <= 5.5e-5:
		tmp = 1.0 - y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -90.0)
		tmp = x;
	elseif (y <= -5.8e-105)
		tmp = Float64(y * x);
	elseif (y <= 6.2e-123)
		tmp = 1.0;
	elseif (y <= 1.15e-50)
		tmp = Float64(y * x);
	elseif (y <= 5.5e-5)
		tmp = Float64(1.0 - y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -90.0)
		tmp = x;
	elseif (y <= -5.8e-105)
		tmp = y * x;
	elseif (y <= 6.2e-123)
		tmp = 1.0;
	elseif (y <= 1.15e-50)
		tmp = y * x;
	elseif (y <= 5.5e-5)
		tmp = 1.0 - y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -90.0], x, If[LessEqual[y, -5.8e-105], N[(y * x), $MachinePrecision], If[LessEqual[y, 6.2e-123], 1.0, If[LessEqual[y, 1.15e-50], N[(y * x), $MachinePrecision], If[LessEqual[y, 5.5e-5], N[(1.0 - y), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -90 or 5.5000000000000002e-5 < y

   1. Initial program 34.4%

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

      1. associate-*l/ 54.5%

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

      2. +-commutative 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in y around inf 67.2%

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

   if -90 < y < -5.80000000000000007e-105 or 6.19999999999999996e-123 < y < 1.1500000000000001e-50

   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%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 61.1%

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

      1. /-rgt-identity 61.1%

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

      2. associate-/r/ 60.9%

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

      3. associate-/r* 60.9%

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

      4. +-commutative 60.9%

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

      5. distribute-lft-in 60.9%

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

      6. lft-mult-inverse 60.9%

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

      7. *-rgt-identity 60.9%

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

   6. Simplified 60.9%

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

   7. Taylor expanded in y around 0 58.5%

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

      1. *-commutative 58.5%

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

   9. Simplified 58.5%

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

   if -5.80000000000000007e-105 < y < 6.19999999999999996e-123

   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%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 90.6%

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

   if 1.1500000000000001e-50 < y < 5.5000000000000002e-5

   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%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 68.9%

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

   5. Taylor expanded in y around 0 68.9%

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

      1. neg-mul-1 68.9%

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

      2. unsub-neg 68.9%

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

   7. Simplified 68.9%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -90:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-105}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-123}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-50}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 71.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{y + 1}\\ \mathbf{if}\;y \leq -4 \cdot 10^{-104}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-123}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+97}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+125}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (/ y (+ y 1.0)))))
   (if (<= y -4e-104)
     t_0
     (if (<= y 6.2e-123)
       1.0
       (if (<= y 2.85e+97) t_0 (if (<= y 9.5e+125) (/ 1.0 y) x))))))

C

double code(double x, double y) {
	double t_0 = x * (y / (y + 1.0));
	double tmp;
	if (y <= -4e-104) {
		tmp = t_0;
	} else if (y <= 6.2e-123) {
		tmp = 1.0;
	} else if (y <= 2.85e+97) {
		tmp = t_0;
	} else if (y <= 9.5e+125) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x * (y / (y + 1.0d0))
    if (y <= (-4d-104)) then
        tmp = t_0
    else if (y <= 6.2d-123) then
        tmp = 1.0d0
    else if (y <= 2.85d+97) then
        tmp = t_0
    else if (y <= 9.5d+125) then
        tmp = 1.0d0 / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (y / (y + 1.0));
	double tmp;
	if (y <= -4e-104) {
		tmp = t_0;
	} else if (y <= 6.2e-123) {
		tmp = 1.0;
	} else if (y <= 2.85e+97) {
		tmp = t_0;
	} else if (y <= 9.5e+125) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (y / (y + 1.0))
	tmp = 0
	if y <= -4e-104:
		tmp = t_0
	elif y <= 6.2e-123:
		tmp = 1.0
	elif y <= 2.85e+97:
		tmp = t_0
	elif y <= 9.5e+125:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(y / Float64(y + 1.0)))
	tmp = 0.0
	if (y <= -4e-104)
		tmp = t_0;
	elseif (y <= 6.2e-123)
		tmp = 1.0;
	elseif (y <= 2.85e+97)
		tmp = t_0;
	elseif (y <= 9.5e+125)
		tmp = Float64(1.0 / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (y / (y + 1.0));
	tmp = 0.0;
	if (y <= -4e-104)
		tmp = t_0;
	elseif (y <= 6.2e-123)
		tmp = 1.0;
	elseif (y <= 2.85e+97)
		tmp = t_0;
	elseif (y <= 9.5e+125)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e-104], t$95$0, If[LessEqual[y, 6.2e-123], 1.0, If[LessEqual[y, 2.85e+97], t$95$0, If[LessEqual[y, 9.5e+125], N[(1.0 / y), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.99999999999999971e-104 or 6.19999999999999996e-123 < y < 2.8500000000000001e97

   1. Initial program 62.5%

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

      1. associate-*l/ 71.3%

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

      2. +-commutative 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in x around inf 56.9%

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

      1. associate-*r/ 65.9%

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

      2. *-commutative 65.9%

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

   6. Simplified 65.9%

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

   if -3.99999999999999971e-104 < y < 6.19999999999999996e-123

   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%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 90.6%

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

   if 2.8500000000000001e97 < y < 9.50000000000000041e125

   1. Initial program 16.1%

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

      1. associate-*l/ 16.3%

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

      2. +-commutative 16.3%

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

   3. Simplified 16.3%

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

   4. Taylor expanded in y around -inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in x around 0 74.9%

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

   if 9.50000000000000041e125 < y

   1. Initial program 24.1%

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

      1. associate-*l/ 66.3%

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

      2. +-commutative 66.3%

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

   3. Simplified 66.3%

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

   4. Taylor expanded in y around inf 78.8%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-123}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+125}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{y + 1}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-6}:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+97}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+125}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (/ y (+ y 1.0)))))
   (if (<= y -4.2e-5)
     t_0
     (if (<= y 7.8e-6)
       (+ 1.0 (* y (+ x -1.0)))
       (if (<= y 2.75e+97) t_0 (if (<= y 9e+125) (/ 1.0 y) x))))))

C

double code(double x, double y) {
	double t_0 = x * (y / (y + 1.0));
	double tmp;
	if (y <= -4.2e-5) {
		tmp = t_0;
	} else if (y <= 7.8e-6) {
		tmp = 1.0 + (y * (x + -1.0));
	} else if (y <= 2.75e+97) {
		tmp = t_0;
	} else if (y <= 9e+125) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x * (y / (y + 1.0d0))
    if (y <= (-4.2d-5)) then
        tmp = t_0
    else if (y <= 7.8d-6) then
        tmp = 1.0d0 + (y * (x + (-1.0d0)))
    else if (y <= 2.75d+97) then
        tmp = t_0
    else if (y <= 9d+125) then
        tmp = 1.0d0 / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (y / (y + 1.0));
	double tmp;
	if (y <= -4.2e-5) {
		tmp = t_0;
	} else if (y <= 7.8e-6) {
		tmp = 1.0 + (y * (x + -1.0));
	} else if (y <= 2.75e+97) {
		tmp = t_0;
	} else if (y <= 9e+125) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (y / (y + 1.0))
	tmp = 0
	if y <= -4.2e-5:
		tmp = t_0
	elif y <= 7.8e-6:
		tmp = 1.0 + (y * (x + -1.0))
	elif y <= 2.75e+97:
		tmp = t_0
	elif y <= 9e+125:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(y / Float64(y + 1.0)))
	tmp = 0.0
	if (y <= -4.2e-5)
		tmp = t_0;
	elseif (y <= 7.8e-6)
		tmp = Float64(1.0 + Float64(y * Float64(x + -1.0)));
	elseif (y <= 2.75e+97)
		tmp = t_0;
	elseif (y <= 9e+125)
		tmp = Float64(1.0 / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (y / (y + 1.0));
	tmp = 0.0;
	if (y <= -4.2e-5)
		tmp = t_0;
	elseif (y <= 7.8e-6)
		tmp = 1.0 + (y * (x + -1.0));
	elseif (y <= 2.75e+97)
		tmp = t_0;
	elseif (y <= 9e+125)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e-5], t$95$0, If[LessEqual[y, 7.8e-6], N[(1.0 + N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.75e+97], t$95$0, If[LessEqual[y, 9e+125], N[(1.0 / y), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.19999999999999977e-5 or 7.7999999999999999e-6 < y < 2.75000000000000011e97

   1. Initial program 41.3%

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

      1. associate-*l/ 55.1%

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

      2. +-commutative 55.1%

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

   3. Simplified 55.1%

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

   4. Taylor expanded in x around inf 58.0%

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

      1. associate-*r/ 72.0%

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

      2. *-commutative 72.0%

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

   6. Simplified 72.0%

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

   if -4.19999999999999977e-5 < y < 7.7999999999999999e-6

   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%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.9%

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

   if 2.75000000000000011e97 < y < 9.0000000000000001e125

   1. Initial program 16.1%

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

      1. associate-*l/ 16.3%

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

      2. +-commutative 16.3%

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

   3. Simplified 16.3%

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

   4. Taylor expanded in y around -inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in x around 0 74.9%

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

   if 9.0000000000000001e125 < y

   1. Initial program 24.1%

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

      1. associate-*l/ 66.3%

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

      2. +-commutative 66.3%

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

   3. Simplified 66.3%

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

   4. Taylor expanded in y around inf 78.8%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-6}:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+125}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 71.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -90:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-104}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.24 \cdot 10^{-123}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-50}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -90.0)
   x
   (if (<= y -3.4e-104)
     (* y x)
     (if (<= y 1.24e-123)
       1.0
       (if (<= y 1.05e-50) (* y x) (if (<= y 5.5e-5) 1.0 x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -90.0) {
		tmp = x;
	} else if (y <= -3.4e-104) {
		tmp = y * x;
	} else if (y <= 1.24e-123) {
		tmp = 1.0;
	} else if (y <= 1.05e-50) {
		tmp = y * x;
	} else if (y <= 5.5e-5) {
		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 <= (-90.0d0)) then
        tmp = x
    else if (y <= (-3.4d-104)) then
        tmp = y * x
    else if (y <= 1.24d-123) then
        tmp = 1.0d0
    else if (y <= 1.05d-50) then
        tmp = y * x
    else if (y <= 5.5d-5) 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 <= -90.0) {
		tmp = x;
	} else if (y <= -3.4e-104) {
		tmp = y * x;
	} else if (y <= 1.24e-123) {
		tmp = 1.0;
	} else if (y <= 1.05e-50) {
		tmp = y * x;
	} else if (y <= 5.5e-5) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -90.0:
		tmp = x
	elif y <= -3.4e-104:
		tmp = y * x
	elif y <= 1.24e-123:
		tmp = 1.0
	elif y <= 1.05e-50:
		tmp = y * x
	elif y <= 5.5e-5:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -90.0)
		tmp = x;
	elseif (y <= -3.4e-104)
		tmp = Float64(y * x);
	elseif (y <= 1.24e-123)
		tmp = 1.0;
	elseif (y <= 1.05e-50)
		tmp = Float64(y * x);
	elseif (y <= 5.5e-5)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -90.0)
		tmp = x;
	elseif (y <= -3.4e-104)
		tmp = y * x;
	elseif (y <= 1.24e-123)
		tmp = 1.0;
	elseif (y <= 1.05e-50)
		tmp = y * x;
	elseif (y <= 5.5e-5)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -90.0], x, If[LessEqual[y, -3.4e-104], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.24e-123], 1.0, If[LessEqual[y, 1.05e-50], N[(y * x), $MachinePrecision], If[LessEqual[y, 5.5e-5], 1.0, x]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -90 or 5.5000000000000002e-5 < y

   1. Initial program 34.4%

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

      1. associate-*l/ 54.5%

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

      2. +-commutative 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in y around inf 67.2%

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

   if -90 < y < -3.40000000000000015e-104 or 1.2399999999999999e-123 < y < 1.05e-50

   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%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 61.1%

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

      1. /-rgt-identity 61.1%

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

      2. associate-/r/ 60.9%

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

      3. associate-/r* 60.9%

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

      4. +-commutative 60.9%

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

      5. distribute-lft-in 60.9%

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

      6. lft-mult-inverse 60.9%

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

      7. *-rgt-identity 60.9%

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

   6. Simplified 60.9%

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

   7. Taylor expanded in y around 0 58.5%

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

      1. *-commutative 58.5%

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

   9. Simplified 58.5%

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

   if -3.40000000000000015e-104 < y < 1.2399999999999999e-123 or 1.05e-50 < y < 5.5000000000000002e-5

   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%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 87.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -90:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-104}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.24 \cdot 10^{-123}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-50}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 33.8%

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

      1. associate-*l/ 54.1%

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

      2. +-commutative 54.1%

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

   3. Simplified 54.1%

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

   4. Taylor expanded in y around -inf 97.4%

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

      1. mul-1-neg 97.4%

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

      2. unsub-neg 97.4%

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

      3. sub-neg 97.4%

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

      4. metadata-eval 97.4%

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

   6. Simplified 97.4%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 97.8%

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

4. Final simplification 97.6%

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

Alternative 12: 74.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 5.5e-5) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 5.5e-5) {
		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 <= 5.5d-5) 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 <= 5.5e-5) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 5.5e-5:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 5.5e-5)
		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 <= 5.5e-5)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 5.5e-5], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 5.5000000000000002e-5 < y

   1. Initial program 34.8%

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

      1. associate-*l/ 54.7%

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

      2. +-commutative 54.7%

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

   3. Simplified 54.7%

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

   4. Taylor expanded in y around inf 66.7%

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

   if -1 < y < 5.5000000000000002e-5

   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%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 69.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 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 66.6%

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

   1. associate-*l/ 76.8%

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

   2. +-commutative 76.8%

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

3. Simplified 76.8%

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

4. Taylor expanded in y around 0 36.2%

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

5. Final simplification 36.2%

   \[\leadsto 1 \]

Developer target: 99.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 / y) - ((x / y) - x)
    if (y < (-3693.8482788297247d0)) then
        tmp = t_0
    else if (y < 6799310503.41891d0) then
        tmp = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023318 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

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

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