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

Percentage Accurate: 66.5% → 99.2%

Time: 7.2s

Alternatives: 10

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: 66.5% 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: 99.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+27}:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq 128000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{x + -1}{y + 1}, y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.55e+27)
   (- x (/ -1.0 y))
   (if (<= y 128000000.0)
     (fma (/ (+ x -1.0) (+ y 1.0)) y 1.0)
     (+ x (/ (- 1.0 x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.55e+27) {
		tmp = x - (-1.0 / y);
	} else if (y <= 128000000.0) {
		tmp = fma(((x + -1.0) / (y + 1.0)), y, 1.0);
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.55e+27)
		tmp = Float64(x - Float64(-1.0 / y));
	elseif (y <= 128000000.0)
		tmp = fma(Float64(Float64(x + -1.0) / Float64(y + 1.0)), y, 1.0);
	else
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.55e+27], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 128000000.0], N[(N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * y + 1.0), $MachinePrecision], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.54999999999999998e27

   1. Initial program 27.5%

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

      1. associate-*l/ 52.4%

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

      2. +-commutative 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. distribute-neg-frac 100.0%

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

      8. metadata-eval 100.0%

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

      9. sub-neg 100.0%

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

      10. unsub-neg 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

   if -1.54999999999999998e27 < y < 1.28e8

   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%

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

      4. distribute-neg-frac 99.9%

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

      5. associate-/r/ 99.9%

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

      6. fma-def 100.0%

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

      7. neg-sub0 100.0%

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

      8. associate--r- 100.0%

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

      9. metadata-eval 100.0%

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

      10. +-commutative 100.0%

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

      11. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   if 1.28e8 < y

   1. Initial program 36.3%

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

      1. associate-*l/ 62.9%

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

      2. +-commutative 62.9%

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

   3. Simplified 62.9%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. distribute-neg-frac 100.0%

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

      8. metadata-eval 100.0%

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

      9. sub-neg 100.0%

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

      10. unsub-neg 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+27}:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq 128000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{x + -1}{y + 1}, y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-53}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-55}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-9}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y -6.2e-53)
     (* y x)
     (if (<= y 1.62e-55) 1.0 (if (<= y 1.55e-9) (* y x) x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= -6.2e-53) {
		tmp = y * x;
	} else if (y <= 1.62e-55) {
		tmp = 1.0;
	} else if (y <= 1.55e-9) {
		tmp = y * x;
	} 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 <= (-6.2d-53)) then
        tmp = y * x
    else if (y <= 1.62d-55) then
        tmp = 1.0d0
    else if (y <= 1.55d-9) then
        tmp = y * x
    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 <= -6.2e-53) {
		tmp = y * x;
	} else if (y <= 1.62e-55) {
		tmp = 1.0;
	} else if (y <= 1.55e-9) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= -6.2e-53:
		tmp = y * x
	elif y <= 1.62e-55:
		tmp = 1.0
	elif y <= 1.55e-9:
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= -6.2e-53)
		tmp = Float64(y * x);
	elseif (y <= 1.62e-55)
		tmp = 1.0;
	elseif (y <= 1.55e-9)
		tmp = Float64(y * x);
	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 <= -6.2e-53)
		tmp = y * x;
	elseif (y <= 1.62e-55)
		tmp = 1.0;
	elseif (y <= 1.55e-9)
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, -6.2e-53], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.62e-55], 1.0, If[LessEqual[y, 1.55e-9], N[(y * x), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1.55000000000000002e-9 < y

   1. Initial program 35.1%

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

      1. associate-*l/ 59.7%

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

      2. +-commutative 59.7%

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

   3. Simplified 59.7%

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

   5. Taylor expanded in y around inf 76.7%

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

   if -1 < y < -6.20000000000000031e-53 or 1.62000000000000006e-55 < y < 1.55000000000000002e-9

   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. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 99.7%

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

      2. clear-num 99.4%

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

      3. un-div-inv 99.1%

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

   6. Applied egg-rr 99.1%

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

   7. Taylor expanded in x around inf 89.0%

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

      1. *-commutative 89.0%

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

   9. Simplified 89.0%

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

   10. Taylor expanded in y around 0 78.5%

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

   if -6.20000000000000031e-53 < y < 1.62000000000000006e-55

   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. Add Preprocessing

   5. Taylor expanded in y around 0 85.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-53}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-55}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-9}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+27}:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq 340000000:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.55e+27)
   (- x (/ -1.0 y))
   (if (<= y 340000000.0)
     (+ 1.0 (* y (/ (+ x -1.0) (+ y 1.0))))
     (+ x (/ (- 1.0 x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.55e+27) {
		tmp = x - (-1.0 / y);
	} else if (y <= 340000000.0) {
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.55d+27)) then
        tmp = x - ((-1.0d0) / y)
    else if (y <= 340000000.0d0) then
        tmp = 1.0d0 + (y * ((x + (-1.0d0)) / (y + 1.0d0)))
    else
        tmp = x + ((1.0d0 - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.55e+27) {
		tmp = x - (-1.0 / y);
	} else if (y <= 340000000.0) {
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.55e+27:
		tmp = x - (-1.0 / y)
	elif y <= 340000000.0:
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)))
	else:
		tmp = x + ((1.0 - x) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.55e+27)
		tmp = Float64(x - Float64(-1.0 / y));
	elseif (y <= 340000000.0)
		tmp = Float64(1.0 + Float64(y * Float64(Float64(x + -1.0) / Float64(y + 1.0))));
	else
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.55e+27)
		tmp = x - (-1.0 / y);
	elseif (y <= 340000000.0)
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	else
		tmp = x + ((1.0 - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.55e+27], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 340000000.0], N[(1.0 + N[(y * N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.54999999999999998e27

   1. Initial program 27.5%

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

      1. associate-*l/ 52.4%

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

      2. +-commutative 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. distribute-neg-frac 100.0%

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

      8. metadata-eval 100.0%

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

      9. sub-neg 100.0%

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

      10. unsub-neg 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

   if -1.54999999999999998e27 < y < 3.4e8

   1. Initial program 99.9%

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

      1. associate-*l/ 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   if 3.4e8 < y

   1. Initial program 36.3%

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

      1. associate-*l/ 62.9%

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

      2. +-commutative 62.9%

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

   3. Simplified 62.9%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. distribute-neg-frac 100.0%

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

      8. metadata-eval 100.0%

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

      9. sub-neg 100.0%

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

      10. unsub-neg 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+27}:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq 340000000:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+27}:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq 58000:\\ \;\;\;\;1 - \frac{y}{\frac{-1 - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.55e+27)
   (- x (/ -1.0 y))
   (if (<= y 58000.0) (- 1.0 (/ y (/ (- -1.0 y) x))) (+ x (/ (- 1.0 x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.55e+27) {
		tmp = x - (-1.0 / y);
	} else if (y <= 58000.0) {
		tmp = 1.0 - (y / ((-1.0 - y) / x));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.55d+27)) then
        tmp = x - ((-1.0d0) / y)
    else if (y <= 58000.0d0) then
        tmp = 1.0d0 - (y / (((-1.0d0) - y) / x))
    else
        tmp = x + ((1.0d0 - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.55e+27) {
		tmp = x - (-1.0 / y);
	} else if (y <= 58000.0) {
		tmp = 1.0 - (y / ((-1.0 - y) / x));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.55e+27:
		tmp = x - (-1.0 / y)
	elif y <= 58000.0:
		tmp = 1.0 - (y / ((-1.0 - y) / x))
	else:
		tmp = x + ((1.0 - x) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.55e+27)
		tmp = Float64(x - Float64(-1.0 / y));
	elseif (y <= 58000.0)
		tmp = Float64(1.0 - Float64(y / Float64(Float64(-1.0 - y) / x)));
	else
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.55e+27)
		tmp = x - (-1.0 / y);
	elseif (y <= 58000.0)
		tmp = 1.0 - (y / ((-1.0 - y) / x));
	else
		tmp = x + ((1.0 - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.55e+27], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 58000.0], N[(1.0 - N[(y / N[(N[(-1.0 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.54999999999999998e27

   1. Initial program 27.5%

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

      1. associate-*l/ 52.4%

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

      2. +-commutative 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. distribute-neg-frac 100.0%

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

      8. metadata-eval 100.0%

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

      9. sub-neg 100.0%

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

      10. unsub-neg 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

   if -1.54999999999999998e27 < y < 58000

   1. Initial program 99.9%

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

      1. associate-*l/ 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 99.2%

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

      1. associate-*r/ 99.2%

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

      2. neg-mul-1 99.2%

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

      3. distribute-neg-in 99.2%

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

      4. metadata-eval 99.2%

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

      5. unsub-neg 99.2%

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

   9. Simplified 99.2%

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

   if 58000 < y

   1. Initial program 36.3%

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

      1. associate-*l/ 62.9%

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

      2. +-commutative 62.9%

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

   3. Simplified 62.9%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. distribute-neg-frac 100.0%

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

      8. metadata-eval 100.0%

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

      9. sub-neg 100.0%

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

      10. unsub-neg 100.0%

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

      11. sub-neg 100.0%

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

      12. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+27}:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq 58000:\\ \;\;\;\;1 - \frac{y}{\frac{-1 - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 0.78d0))) then
        tmp = x - ((-1.0d0) / y)
    else
        tmp = 1.0d0 + (y * (x + (-1.0d0)))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.78000000000000003 < y

   1. Initial program 34.6%

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

      1. associate-*l/ 59.4%

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

      2. +-commutative 59.4%

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

   3. Simplified 59.4%

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

   5. Taylor expanded in y around inf 99.1%

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

      1. associate--l+ 99.1%

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

      2. div-sub 99.1%

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

      3. sub-neg 99.1%

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

      4. +-commutative 99.1%

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

      5. metadata-eval 99.1%

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

      6. distribute-neg-in 99.1%

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

      7. distribute-neg-frac 99.1%

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

      8. metadata-eval 99.1%

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

      9. sub-neg 99.1%

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

      10. unsub-neg 99.1%

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

      11. sub-neg 99.1%

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

      12. metadata-eval 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in x around 0 98.9%

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

   if -1 < y < 0.78000000000000003

   1. Initial program 99.9%

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

      1. associate-*l/ 100.0%

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

      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. Add Preprocessing

   5. Taylor expanded in y around 0 98.5%

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

4. Final simplification 98.7%

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

Alternative 6: 98.2% accurate, 0.6× speedup

Math

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

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 34.6%

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

      1. associate-*l/ 59.4%

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

      2. +-commutative 59.4%

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

   3. Simplified 59.4%

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

   5. Taylor expanded in y around inf 99.1%

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

      1. associate--l+ 99.1%

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

      2. div-sub 99.1%

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

      3. sub-neg 99.1%

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

      4. +-commutative 99.1%

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

      5. metadata-eval 99.1%

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

      6. distribute-neg-in 99.1%

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

      7. distribute-neg-frac 99.1%

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

      8. metadata-eval 99.1%

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

      9. sub-neg 99.1%

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

      10. unsub-neg 99.1%

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

      11. sub-neg 99.1%

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

      12. metadata-eval 99.1%

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

   7. Simplified 99.1%

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

   if -1 < y < 1

   1. Initial program 99.9%

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

      1. associate-*l/ 100.0%

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

      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. Add Preprocessing

   5. Taylor expanded in y around 0 98.5%

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

4. Final simplification 98.8%

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

Alternative 7: 97.7% accurate, 0.7× speedup

Math

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

FPCore

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

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 + (y * x);
	}
	return tmp;
}

Fortran

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

Java

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 34.6%

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

      1. associate-*l/ 59.4%

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

      2. +-commutative 59.4%

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

   3. Simplified 59.4%

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

   5. Taylor expanded in y around inf 99.1%

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

      1. associate--l+ 99.1%

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

      2. div-sub 99.1%

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

      3. sub-neg 99.1%

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

      4. +-commutative 99.1%

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

      5. metadata-eval 99.1%

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

      6. distribute-neg-in 99.1%

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

      7. distribute-neg-frac 99.1%

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

      8. metadata-eval 99.1%

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

      9. sub-neg 99.1%

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

      10. unsub-neg 99.1%

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

      11. sub-neg 99.1%

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

      12. metadata-eval 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in x around 0 98.9%

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

   if -1 < y < 1

   1. Initial program 99.9%

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

      1. associate-*l/ 100.0%

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

      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. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 99.2%

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

      1. associate-*r/ 99.2%

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

      2. neg-mul-1 99.2%

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

      3. distribute-neg-in 99.2%

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

      4. metadata-eval 99.2%

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

      5. unsub-neg 99.2%

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

   9. Simplified 99.2%

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

   10. Taylor expanded in y around 0 97.9%

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

4. Final simplification 98.4%

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

Alternative 8: 86.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 48:\\ \;\;\;\;1 + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 48.0) (+ 1.0 (* y x)) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 48.0) {
		tmp = 1.0 + (y * x);
	} 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 <= 48.0d0) then
        tmp = 1.0d0 + (y * x)
    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 <= 48.0) {
		tmp = 1.0 + (y * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 48.0:
		tmp = 1.0 + (y * x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 48.0)
		tmp = Float64(1.0 + Float64(y * x));
	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 <= 48.0)
		tmp = 1.0 + (y * x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 48.0], N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 48 < y

   1. Initial program 34.6%

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

      1. associate-*l/ 59.4%

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

      2. +-commutative 59.4%

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

   3. Simplified 59.4%

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

   5. Taylor expanded in y around inf 77.3%

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

   if -1 < y < 48

   1. Initial program 99.9%

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

      1. associate-*l/ 100.0%

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

      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. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 99.2%

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

      1. associate-*r/ 99.2%

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

      2. neg-mul-1 99.2%

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

      3. distribute-neg-in 99.2%

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

      4. metadata-eval 99.2%

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

      5. unsub-neg 99.2%

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

   9. Simplified 99.2%

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

   10. Taylor expanded in y around 0 97.9%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 48:\\ \;\;\;\;1 + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.052:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 0.052) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.052) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = x
    else if (y <= 0.052d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.052) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.052:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.052)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.052)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 0.052], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.0519999999999999976 < y

   1. Initial program 34.6%

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

      1. associate-*l/ 59.4%

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

      2. +-commutative 59.4%

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

   3. Simplified 59.4%

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

   5. Taylor expanded in y around inf 77.3%

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

   if -1 < y < 0.0519999999999999976

   1. Initial program 99.9%

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

      1. associate-*l/ 100.0%

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

      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. Add Preprocessing

   5. Taylor expanded in y around 0 74.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.052:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.7% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

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

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 67.3%

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

   1. associate-*l/ 79.7%

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

   2. +-commutative 79.7%

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

3. Simplified 79.7%

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

5. Taylor expanded in y around 0 39.3%

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

6. Final simplification 39.3%

   \[\leadsto 1 \]
7. Add Preprocessing

Developer target: 99.6% 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 2024019 
(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))))