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

Percentage Accurate: 65.5% → 99.1%

Time: 7.9s

Alternatives: 11

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: 65.5% 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: 99.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{1 + y}\\ \mathbf{if}\;t_0 \leq 10^{-9} \lor \neg \left(t_0 \leq 2\right):\\ \;\;\;\;1 + \frac{y}{1 + y} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\frac{1}{y} + \frac{x}{{y}^{2}}\right)\right) + \left(\frac{-1}{{y}^{2}} - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (- 1.0 x) y) (+ 1.0 y))))
   (if (or (<= t_0 1e-9) (not (<= t_0 2.0)))
     (+ 1.0 (* (/ y (+ 1.0 y)) (+ x -1.0)))
     (+
      (+ x (+ (/ 1.0 y) (/ x (pow y 2.0))))
      (- (/ -1.0 (pow y 2.0)) (/ x y))))))

C

double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double tmp;
	if ((t_0 <= 1e-9) || !(t_0 <= 2.0)) {
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	} else {
		tmp = (x + ((1.0 / y) + (x / pow(y, 2.0)))) + ((-1.0 / pow(y, 2.0)) - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((1.0d0 - x) * y) / (1.0d0 + y)
    if ((t_0 <= 1d-9) .or. (.not. (t_0 <= 2.0d0))) then
        tmp = 1.0d0 + ((y / (1.0d0 + y)) * (x + (-1.0d0)))
    else
        tmp = (x + ((1.0d0 / y) + (x / (y ** 2.0d0)))) + (((-1.0d0) / (y ** 2.0d0)) - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double tmp;
	if ((t_0 <= 1e-9) || !(t_0 <= 2.0)) {
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	} else {
		tmp = (x + ((1.0 / y) + (x / Math.pow(y, 2.0)))) + ((-1.0 / Math.pow(y, 2.0)) - (x / y));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((1.0 - x) * y) / (1.0 + y)
	tmp = 0
	if (t_0 <= 1e-9) or not (t_0 <= 2.0):
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0))
	else:
		tmp = (x + ((1.0 / y) + (x / math.pow(y, 2.0)))) + ((-1.0 / math.pow(y, 2.0)) - (x / y))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(1.0 - x) * y) / Float64(1.0 + y))
	tmp = 0.0
	if ((t_0 <= 1e-9) || !(t_0 <= 2.0))
		tmp = Float64(1.0 + Float64(Float64(y / Float64(1.0 + y)) * Float64(x + -1.0)));
	else
		tmp = Float64(Float64(x + Float64(Float64(1.0 / y) + Float64(x / (y ^ 2.0)))) + Float64(Float64(-1.0 / (y ^ 2.0)) - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((1.0 - x) * y) / (1.0 + y);
	tmp = 0.0;
	if ((t_0 <= 1e-9) || ~((t_0 <= 2.0)))
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	else
		tmp = (x + ((1.0 / y) + (x / (y ^ 2.0)))) + ((-1.0 / (y ^ 2.0)) - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 1e-9], N[Not[LessEqual[t$95$0, 2.0]], $MachinePrecision]], N[(1.0 + N[(N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(1.0 / y), $MachinePrecision] + N[(x / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision] - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)) < 1.00000000000000006e-9 or 2 < (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

   1. Initial program 80.9%

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

      1. *-commutative 80.9%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   if 1.00000000000000006e-9 < (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)) < 2

   1. Initial program 10.2%

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

      1. sub-neg 10.2%

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

      2. +-commutative 10.2%

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

      3. associate-/l* 10.3%

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

      4. distribute-neg-frac 10.3%

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

      5. associate-/r/ 10.0%

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

      6. fma-def 9.7%

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

      7. neg-sub0 9.7%

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

      8. associate--r- 9.7%

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

      9. metadata-eval 9.7%

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

      10. +-commutative 9.7%

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

      11. +-commutative 9.7%

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

   3. Simplified 9.7%

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

   4. Taylor expanded in y around inf 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 10^{-9} \lor \neg \left(\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 2\right):\\ \;\;\;\;1 + \frac{y}{1 + y} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\frac{1}{y} + \frac{x}{{y}^{2}}\right)\right) + \left(\frac{-1}{{y}^{2}} - \frac{x}{y}\right)\\ \end{array} \]

Alternative 2: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{1 + y}\\ \mathbf{if}\;t_0 \leq 10^{-9} \lor \neg \left(t_0 \leq 2\right):\\ \;\;\;\;1 + \frac{y}{1 + y} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x + -1}{y} \cdot \left(\frac{1}{y} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (- 1.0 x) y) (+ 1.0 y))))
   (if (or (<= t_0 1e-9) (not (<= t_0 2.0)))
     (+ 1.0 (* (/ y (+ 1.0 y)) (+ x -1.0)))
     (+ x (* (/ (+ x -1.0) y) (+ (/ 1.0 y) -1.0))))))

C

double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double tmp;
	if ((t_0 <= 1e-9) || !(t_0 <= 2.0)) {
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	} else {
		tmp = x + (((x + -1.0) / y) * ((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) :: t_0
    real(8) :: tmp
    t_0 = ((1.0d0 - x) * y) / (1.0d0 + y)
    if ((t_0 <= 1d-9) .or. (.not. (t_0 <= 2.0d0))) then
        tmp = 1.0d0 + ((y / (1.0d0 + y)) * (x + (-1.0d0)))
    else
        tmp = x + (((x + (-1.0d0)) / y) * ((1.0d0 / y) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double tmp;
	if ((t_0 <= 1e-9) || !(t_0 <= 2.0)) {
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	} else {
		tmp = x + (((x + -1.0) / y) * ((1.0 / y) + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((1.0 - x) * y) / (1.0 + y)
	tmp = 0
	if (t_0 <= 1e-9) or not (t_0 <= 2.0):
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0))
	else:
		tmp = x + (((x + -1.0) / y) * ((1.0 / y) + -1.0))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(1.0 - x) * y) / Float64(1.0 + y))
	tmp = 0.0
	if ((t_0 <= 1e-9) || !(t_0 <= 2.0))
		tmp = Float64(1.0 + Float64(Float64(y / Float64(1.0 + y)) * Float64(x + -1.0)));
	else
		tmp = Float64(x + Float64(Float64(Float64(x + -1.0) / y) * Float64(Float64(1.0 / y) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((1.0 - x) * y) / (1.0 + y);
	tmp = 0.0;
	if ((t_0 <= 1e-9) || ~((t_0 <= 2.0)))
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	else
		tmp = x + (((x + -1.0) / y) * ((1.0 / y) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 1e-9], N[Not[LessEqual[t$95$0, 2.0]], $MachinePrecision]], N[(1.0 + N[(N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision] * N[(N[(1.0 / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)) < 1.00000000000000006e-9 or 2 < (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

   1. Initial program 80.9%

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

      1. *-commutative 80.9%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   if 1.00000000000000006e-9 < (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)) < 2

   1. Initial program 10.2%

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

      1. *-commutative 10.2%

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

      2. associate-*l/ 10.2%

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

      3. +-commutative 10.2%

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

   3. Simplified 10.2%

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

   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%

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

      1. *-un-lft-identity 100.0%

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

      2. unpow2 100.0%

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

      3. times-frac 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-un-lft-identity 100.0%

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

      3. distribute-rgt-out-- 100.0%

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

   10. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 10^{-9} \lor \neg \left(\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 2\right):\\ \;\;\;\;1 + \frac{y}{1 + y} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x + -1}{y} \cdot \left(\frac{1}{y} + -1\right)\\ \end{array} \]

Alternative 3: 98.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{1 + y}\\ \mathbf{if}\;t_0 \leq 10^{-9} \lor \neg \left(t_0 \leq 2\right):\\ \;\;\;\;1 + \frac{y}{1 + y} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (- 1.0 x) y) (+ 1.0 y))))
   (if (or (<= t_0 1e-9) (not (<= t_0 2.0)))
     (+ 1.0 (* (/ y (+ 1.0 y)) (+ x -1.0)))
     (- x (/ -1.0 y)))))

C

double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double tmp;
	if ((t_0 <= 1e-9) || !(t_0 <= 2.0)) {
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	} else {
		tmp = x - (-1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((1.0d0 - x) * y) / (1.0d0 + y)
    if ((t_0 <= 1d-9) .or. (.not. (t_0 <= 2.0d0))) then
        tmp = 1.0d0 + ((y / (1.0d0 + y)) * (x + (-1.0d0)))
    else
        tmp = x - ((-1.0d0) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double tmp;
	if ((t_0 <= 1e-9) || !(t_0 <= 2.0)) {
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	} else {
		tmp = x - (-1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((1.0 - x) * y) / (1.0 + y)
	tmp = 0
	if (t_0 <= 1e-9) or not (t_0 <= 2.0):
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0))
	else:
		tmp = x - (-1.0 / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(1.0 - x) * y) / Float64(1.0 + y))
	tmp = 0.0
	if ((t_0 <= 1e-9) || !(t_0 <= 2.0))
		tmp = Float64(1.0 + Float64(Float64(y / Float64(1.0 + y)) * Float64(x + -1.0)));
	else
		tmp = Float64(x - Float64(-1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((1.0 - x) * y) / (1.0 + y);
	tmp = 0.0;
	if ((t_0 <= 1e-9) || ~((t_0 <= 2.0)))
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	else
		tmp = x - (-1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 1e-9], N[Not[LessEqual[t$95$0, 2.0]], $MachinePrecision]], N[(1.0 + N[(N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)) < 1.00000000000000006e-9 or 2 < (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

   1. Initial program 80.9%

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

      1. *-commutative 80.9%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   if 1.00000000000000006e-9 < (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)) < 2

   1. Initial program 10.2%

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

      1. *-commutative 10.2%

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

      2. associate-*l/ 10.2%

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

      3. +-commutative 10.2%

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

   3. Simplified 10.2%

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

   4. Taylor expanded in y around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in x around 0 99.9%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 10^{-9} \lor \neg \left(\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 2\right):\\ \;\;\;\;1 + \frac{y}{1 + y} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-1}{y}\\ \end{array} \]

Alternative 4: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{-1}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-122}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-5}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- x (/ -1.0 y))))
   (if (<= y -1.0)
     t_0
     (if (<= y -1.95e-122) (* x y) (if (<= y 7e-5) (- 1.0 y) t_0)))))

C

double code(double x, double y) {
	double t_0 = x - (-1.0 / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -1.95e-122) {
		tmp = x * y;
	} else if (y <= 7e-5) {
		tmp = 1.0 - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x - ((-1.0d0) / y)
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= (-1.95d-122)) then
        tmp = x * y
    else if (y <= 7d-5) then
        tmp = 1.0d0 - y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x - (-1.0 / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -1.95e-122) {
		tmp = x * y;
	} else if (y <= 7e-5) {
		tmp = 1.0 - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x - (-1.0 / y)
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= -1.95e-122:
		tmp = x * y
	elif y <= 7e-5:
		tmp = 1.0 - y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x - Float64(-1.0 / y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= -1.95e-122)
		tmp = Float64(x * y);
	elseif (y <= 7e-5)
		tmp = Float64(1.0 - y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x - (-1.0 / y);
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= -1.95e-122)
		tmp = x * y;
	elseif (y <= 7e-5)
		tmp = 1.0 - y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, -1.95e-122], N[(x * y), $MachinePrecision], If[LessEqual[y, 7e-5], N[(1.0 - y), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 6.9999999999999994e-5 < y

   1. Initial program 31.2%

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

      1. *-commutative 31.2%

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

      2. associate-*l/ 56.4%

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

      3. +-commutative 56.4%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in y around -inf 99.3%

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

      1. mul-1-neg 99.3%

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

      2. unsub-neg 99.3%

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

      3. sub-neg 99.3%

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

      4. metadata-eval 99.3%

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

   6. Simplified 99.3%

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

   7. Taylor expanded in x around 0 99.2%

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

   if -1 < y < -1.94999999999999995e-122

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l/ 99.9%

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

      3. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 96.3%

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

   5. Taylor expanded in x around inf 62.3%

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

      1. *-commutative 62.3%

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

   7. Simplified 62.3%

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

   if -1.94999999999999995e-122 < y < 6.9999999999999994e-5

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around 0 84.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-122}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-5}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-1}{y}\\ \end{array} \]

Alternative 5: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.8\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.8)))
   (- x (/ -1.0 y))
   (+ 1.0 (* y (+ x -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.8)) {
		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 <= 0.8d0))) 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 <= 0.8)) {
		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 <= 0.8):
		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 <= 0.8))
		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 <= 0.8)))
		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, 0.8]], $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 0.80000000000000004 < y

   1. Initial program 30.7%

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

      1. *-commutative 30.7%

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

      2. associate-*l/ 56.1%

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

      3. +-commutative 56.1%

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

   3. Simplified 56.1%

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

   4. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 99.8%

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

   if -1 < y < 0.80000000000000004

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.9%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.8\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 6: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq 1.05:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   (- x (/ -1.0 y))
   (if (<= y 1.05) (+ 1.0 (* y (+ x -1.0))) (+ x (/ (- 1.0 x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x - (-1.0 / y);
	} else if (y <= 1.05) {
		tmp = 1.0 + (y * (x + -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 <= (-1.0d0)) then
        tmp = x - ((-1.0d0) / y)
    else if (y <= 1.05d0) then
        tmp = 1.0d0 + (y * (x + (-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 <= -1.0) {
		tmp = x - (-1.0 / y);
	} else if (y <= 1.05) {
		tmp = 1.0 + (y * (x + -1.0));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x - (-1.0 / y)
	elif y <= 1.05:
		tmp = 1.0 + (y * (x + -1.0))
	else:
		tmp = x + ((1.0 - x) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(x - Float64(-1.0 / y));
	elseif (y <= 1.05)
		tmp = Float64(1.0 + Float64(y * Float64(x + -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 <= -1.0)
		tmp = x - (-1.0 / y);
	elseif (y <= 1.05)
		tmp = 1.0 + (y * (x + -1.0));
	else
		tmp = x + ((1.0 - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05], N[(1.0 + N[(y * N[(x + -1.0), $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

   1. Initial program 32.2%

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

      1. *-commutative 32.2%

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

      2. associate-*l/ 59.2%

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

      3. +-commutative 59.2%

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

   3. Simplified 59.2%

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

   4. Taylor expanded in y around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in x around 0 99.9%

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

   if -1 < y < 1.05000000000000004

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.9%

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

   if 1.05000000000000004 < y

   1. Initial program 28.9%

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

      1. *-commutative 28.9%

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

      2. associate-*l/ 52.2%

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

      3. +-commutative 52.2%

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

   3. Simplified 52.2%

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

   4. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq 1.05:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \]

Alternative 7: 71.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-122}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-5}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.9e+15)
   x
   (if (<= y -1.4e-122) (* x y) (if (<= y 7e-5) (- 1.0 y) x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.9e+15) {
		tmp = x;
	} else if (y <= -1.4e-122) {
		tmp = x * y;
	} else if (y <= 7e-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 <= (-4.9d+15)) then
        tmp = x
    else if (y <= (-1.4d-122)) then
        tmp = x * y
    else if (y <= 7d-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 <= -4.9e+15) {
		tmp = x;
	} else if (y <= -1.4e-122) {
		tmp = x * y;
	} else if (y <= 7e-5) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.9e+15:
		tmp = x
	elif y <= -1.4e-122:
		tmp = x * y
	elif y <= 7e-5:
		tmp = 1.0 - y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.9e+15)
		tmp = x;
	elseif (y <= -1.4e-122)
		tmp = Float64(x * y);
	elseif (y <= 7e-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 <= -4.9e+15)
		tmp = x;
	elseif (y <= -1.4e-122)
		tmp = x * y;
	elseif (y <= 7e-5)
		tmp = 1.0 - y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.9e+15], x, If[LessEqual[y, -1.4e-122], N[(x * y), $MachinePrecision], If[LessEqual[y, 7e-5], N[(1.0 - y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9e15 or 6.9999999999999994e-5 < y

   1. Initial program 31.3%

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

      1. *-commutative 31.3%

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

      2. associate-*l/ 56.6%

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

      3. +-commutative 56.6%

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

   3. Simplified 56.6%

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

   4. Taylor expanded in y around inf 79.1%

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

   if -4.9e15 < y < -1.3999999999999999e-122

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. associate-*l/ 95.6%

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

      3. +-commutative 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around 0 91.1%

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

   5. Taylor expanded in x around inf 59.1%

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

      1. *-commutative 59.1%

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

   7. Simplified 59.1%

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

   if -1.3999999999999999e-122 < y < 6.9999999999999994e-5

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around 0 84.8%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-122}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-5}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 98.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 30.7%

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

      1. *-commutative 30.7%

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

      2. associate-*l/ 56.1%

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

      3. +-commutative 56.1%

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

   3. Simplified 56.1%

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

   4. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 99.8%

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

   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. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.9%

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

   5. Taylor expanded in x around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. distribute-lft-neg-out 98.9%

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

      3. *-commutative 98.9%

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

   7. Simplified 98.9%

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

4. Final simplification 99.4%

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

Alternative 9: 71.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-126}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.9e+15) x (if (<= y -1.4e-126) (* x y) (if (<= y 7e-5) 1.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.9e+15) {
		tmp = x;
	} else if (y <= -1.4e-126) {
		tmp = x * y;
	} else if (y <= 7e-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 <= (-4.9d+15)) then
        tmp = x
    else if (y <= (-1.4d-126)) then
        tmp = x * y
    else if (y <= 7d-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 <= -4.9e+15) {
		tmp = x;
	} else if (y <= -1.4e-126) {
		tmp = x * y;
	} else if (y <= 7e-5) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.9e+15:
		tmp = x
	elif y <= -1.4e-126:
		tmp = x * y
	elif y <= 7e-5:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.9e+15)
		tmp = x;
	elseif (y <= -1.4e-126)
		tmp = Float64(x * y);
	elseif (y <= 7e-5)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.9e+15)
		tmp = x;
	elseif (y <= -1.4e-126)
		tmp = x * y;
	elseif (y <= 7e-5)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.9e+15], x, If[LessEqual[y, -1.4e-126], N[(x * y), $MachinePrecision], If[LessEqual[y, 7e-5], 1.0, x]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9e15 or 6.9999999999999994e-5 < y

   1. Initial program 31.3%

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

      1. *-commutative 31.3%

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

      2. associate-*l/ 56.6%

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

      3. +-commutative 56.6%

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

   3. Simplified 56.6%

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

   4. Taylor expanded in y around inf 79.1%

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

   if -4.9e15 < y < -1.39999999999999996e-126

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. associate-*l/ 95.6%

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

      3. +-commutative 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around 0 91.1%

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

   5. Taylor expanded in x around inf 59.1%

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

      1. *-commutative 59.1%

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

   7. Simplified 59.1%

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

   if -1.39999999999999996e-126 < y < 6.9999999999999994e-5

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 84.8%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-126}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 74.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 7e-5) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 7e-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 <= 7d-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 <= 7e-5) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 7e-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 <= 7e-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 <= 7e-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, 7e-5], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 6.9999999999999994e-5 < y

   1. Initial program 31.2%

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

      1. *-commutative 31.2%

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

      2. associate-*l/ 56.4%

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

      3. +-commutative 56.4%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in y around inf 78.5%

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

   if -1 < y < 6.9999999999999994e-5

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 77.6%

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

4. Final simplification 78.1%

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

Alternative 11: 38.5% 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 61.8%

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

   1. *-commutative 61.8%

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

   2. associate-*l/ 75.8%

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

   3. +-commutative 75.8%

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

3. Simplified 75.8%

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

4. Taylor expanded in y around 0 36.6%

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

5. Final simplification 36.6%

   \[\leadsto 1 \]

Developer target: 99.6% 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 2023320 
(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))))