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

Percentage Accurate: 65.4% → 99.9%

Time: 48.1s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 65.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -1}{{y}^{2}}\\ \mathbf{if}\;y \leq -320000:\\ \;\;\;\;x + \left(t\_0 + \frac{1 - x}{y}\right)\\ \mathbf{elif}\;y \leq 11500:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x + -1}{y + 1}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{x + -1}{y}\right) + \left(t\_0 + \frac{1 - x}{{y}^{3}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (+ x -1.0) (pow y 2.0))))
   (if (<= y -320000.0)
     (+ x (+ t_0 (/ (- 1.0 x) y)))
     (if (<= y 11500.0)
       (fma y (/ (+ x -1.0) (+ y 1.0)) 1.0)
       (+ (- x (/ (+ x -1.0) y)) (+ t_0 (/ (- 1.0 x) (pow y 3.0))))))))

C

double code(double x, double y) {
	double t_0 = (x + -1.0) / pow(y, 2.0);
	double tmp;
	if (y <= -320000.0) {
		tmp = x + (t_0 + ((1.0 - x) / y));
	} else if (y <= 11500.0) {
		tmp = fma(y, ((x + -1.0) / (y + 1.0)), 1.0);
	} else {
		tmp = (x - ((x + -1.0) / y)) + (t_0 + ((1.0 - x) / pow(y, 3.0)));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(x + -1.0) / (y ^ 2.0))
	tmp = 0.0
	if (y <= -320000.0)
		tmp = Float64(x + Float64(t_0 + Float64(Float64(1.0 - x) / y)));
	elseif (y <= 11500.0)
		tmp = fma(y, Float64(Float64(x + -1.0) / Float64(y + 1.0)), 1.0);
	else
		tmp = Float64(Float64(x - Float64(Float64(x + -1.0) / y)) + Float64(t_0 + Float64(Float64(1.0 - x) / (y ^ 3.0))));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x + -1.0), $MachinePrecision] / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -320000.0], N[(x + N[(t$95$0 + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 11500.0], N[(y * N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(N[(x - N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 + N[(N[(1.0 - x), $MachinePrecision] / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2e5

   1. Initial program 36.3%

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

      1. associate-/l* 57.4%

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

      2. remove-double-neg 57.4%

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

      3. remove-double-neg 57.4%

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

      4. +-commutative 57.4%

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

   3. Simplified 57.4%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. sub-neg 100.0%

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

      4. associate--l+ 100.0%

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

      5. div-sub 100.0%

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

      6. sub-neg 100.0%

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

      7. +-commutative 100.0%

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

      8. neg-mul-1 100.0%

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

      9. metadata-eval 100.0%

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

      10. distribute-lft-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. sub-neg 100.0%

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

      13. associate-*r/ 100.0%

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

      14. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -3.2e5 < y < 11500

   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. *-commutative 99.9%

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

      4. associate-/l* 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. fma-define 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. +-commutative 99.9%

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

      9. distribute-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   if 11500 < y

   1. Initial program 40.7%

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

      1. associate-/l* 53.3%

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

      2. remove-double-neg 53.3%

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

      3. remove-double-neg 53.3%

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

      4. +-commutative 53.3%

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

   3. Simplified 53.3%

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

   5. Taylor expanded in y around -inf 99.9%

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

      1. associate-+r+ 99.9%

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

      2. associate--l+ 99.9%

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

      3. mul-1-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -320000:\\ \;\;\;\;x + \left(\frac{x + -1}{{y}^{2}} + \frac{1 - x}{y}\right)\\ \mathbf{elif}\;y \leq 11500:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x + -1}{y + 1}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{x + -1}{y}\right) + \left(\frac{x + -1}{{y}^{2}} + \frac{1 - x}{{y}^{3}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{if}\;t\_0 \leq 5 \cdot 10^{-14} \lor \neg \left(t\_0 \leq 1.001\right):\\ \;\;\;\;1 + \left(x + -1\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{y} + \frac{-1}{{y}^{2}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ y 1.0))))
   (if (or (<= t_0 5e-14) (not (<= t_0 1.001)))
     (+ 1.0 (* (+ x -1.0) (/ y (+ y 1.0))))
     (+ x (+ (/ 1.0 y) (/ -1.0 (pow y 2.0)))))))

C

double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 5e-14) || !(t_0 <= 1.001)) {
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)));
	} else {
		tmp = x + ((1.0 / y) + (-1.0 / pow(y, 2.0)));
	}
	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 = (y * (1.0d0 - x)) / (y + 1.0d0)
    if ((t_0 <= 5d-14) .or. (.not. (t_0 <= 1.001d0))) then
        tmp = 1.0d0 + ((x + (-1.0d0)) * (y / (y + 1.0d0)))
    else
        tmp = x + ((1.0d0 / y) + ((-1.0d0) / (y ** 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 5e-14) || !(t_0 <= 1.001)) {
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)));
	} else {
		tmp = x + ((1.0 / y) + (-1.0 / Math.pow(y, 2.0)));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (1.0 - x)) / (y + 1.0)
	tmp = 0
	if (t_0 <= 5e-14) or not (t_0 <= 1.001):
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)))
	else:
		tmp = x + ((1.0 / y) + (-1.0 / math.pow(y, 2.0)))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(1.0 - x)) / Float64(y + 1.0))
	tmp = 0.0
	if ((t_0 <= 5e-14) || !(t_0 <= 1.001))
		tmp = Float64(1.0 + Float64(Float64(x + -1.0) * Float64(y / Float64(y + 1.0))));
	else
		tmp = Float64(x + Float64(Float64(1.0 / y) + Float64(-1.0 / (y ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * (1.0 - x)) / (y + 1.0);
	tmp = 0.0;
	if ((t_0 <= 5e-14) || ~((t_0 <= 1.001)))
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)));
	else
		tmp = x + ((1.0 / y) + (-1.0 / (y ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 5e-14], N[Not[LessEqual[t$95$0, 1.001]], $MachinePrecision]], N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 / y), $MachinePrecision] + N[(-1.0 / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)) < 5.0000000000000002e-14 or 1.0009999999999999 < (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

   1. Initial program 88.0%

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

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. remove-double-neg 99.9%

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

      4. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   if 5.0000000000000002e-14 < (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)) < 1.0009999999999999

   1. Initial program 11.8%

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

      1. associate-/l* 11.8%

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

      2. remove-double-neg 11.8%

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

      3. remove-double-neg 11.8%

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

      4. +-commutative 11.8%

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

   3. Simplified 11.8%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. neg-mul-1 99.8%

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

      3. sub-neg 99.8%

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

      4. associate--l+ 99.8%

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

      5. div-sub 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. neg-mul-1 99.8%

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

      9. metadata-eval 99.8%

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

      10. distribute-lft-in 99.8%

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

      11. metadata-eval 99.8%

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

      12. sub-neg 99.8%

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

      13. associate-*r/ 99.8%

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

      14. mul-1-neg 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 5 \cdot 10^{-14} \lor \neg \left(\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 1.001\right):\\ \;\;\;\;1 + \left(x + -1\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{y} + \frac{-1}{{y}^{2}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -250000:\\ \;\;\;\;x + \left(\frac{x + -1}{{y}^{2}} + \frac{1 - x}{y}\right)\\ \mathbf{elif}\;y \leq 7500000:\\ \;\;\;\;1 + \left(x + -1\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{y} + \frac{-1}{{y}^{2}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -250000.0)
   (+ x (+ (/ (+ x -1.0) (pow y 2.0)) (/ (- 1.0 x) y)))
   (if (<= y 7500000.0)
     (+ 1.0 (* (+ x -1.0) (/ y (+ y 1.0))))
     (+ x (+ (/ 1.0 y) (/ -1.0 (pow y 2.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -250000.0) {
		tmp = x + (((x + -1.0) / pow(y, 2.0)) + ((1.0 - x) / y));
	} else if (y <= 7500000.0) {
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)));
	} else {
		tmp = x + ((1.0 / y) + (-1.0 / pow(y, 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-250000.0d0)) then
        tmp = x + (((x + (-1.0d0)) / (y ** 2.0d0)) + ((1.0d0 - x) / y))
    else if (y <= 7500000.0d0) then
        tmp = 1.0d0 + ((x + (-1.0d0)) * (y / (y + 1.0d0)))
    else
        tmp = x + ((1.0d0 / y) + ((-1.0d0) / (y ** 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -250000.0) {
		tmp = x + (((x + -1.0) / Math.pow(y, 2.0)) + ((1.0 - x) / y));
	} else if (y <= 7500000.0) {
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)));
	} else {
		tmp = x + ((1.0 / y) + (-1.0 / Math.pow(y, 2.0)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -250000.0:
		tmp = x + (((x + -1.0) / math.pow(y, 2.0)) + ((1.0 - x) / y))
	elif y <= 7500000.0:
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)))
	else:
		tmp = x + ((1.0 / y) + (-1.0 / math.pow(y, 2.0)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -250000.0)
		tmp = Float64(x + Float64(Float64(Float64(x + -1.0) / (y ^ 2.0)) + Float64(Float64(1.0 - x) / y)));
	elseif (y <= 7500000.0)
		tmp = Float64(1.0 + Float64(Float64(x + -1.0) * Float64(y / Float64(y + 1.0))));
	else
		tmp = Float64(x + Float64(Float64(1.0 / y) + Float64(-1.0 / (y ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -250000.0)
		tmp = x + (((x + -1.0) / (y ^ 2.0)) + ((1.0 - x) / y));
	elseif (y <= 7500000.0)
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)));
	else
		tmp = x + ((1.0 / y) + (-1.0 / (y ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -250000.0], N[(x + N[(N[(N[(x + -1.0), $MachinePrecision] / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7500000.0], N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 / y), $MachinePrecision] + N[(-1.0 / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5e5

   1. Initial program 36.3%

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

      1. associate-/l* 57.4%

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

      2. remove-double-neg 57.4%

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

      3. remove-double-neg 57.4%

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

      4. +-commutative 57.4%

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

   3. Simplified 57.4%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. sub-neg 100.0%

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

      4. associate--l+ 100.0%

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

      5. div-sub 100.0%

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

      6. sub-neg 100.0%

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

      7. +-commutative 100.0%

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

      8. neg-mul-1 100.0%

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

      9. metadata-eval 100.0%

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

      10. distribute-lft-in 100.0%

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

      11. metadata-eval 100.0%

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

      12. sub-neg 100.0%

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

      13. associate-*r/ 100.0%

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

      14. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -2.5e5 < y < 7.5e6

   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%

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

      2. remove-double-neg 99.9%

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

      3. remove-double-neg 99.9%

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

      4. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   if 7.5e6 < y

   1. Initial program 39.7%

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

      1. associate-/l* 52.6%

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

      2. remove-double-neg 52.6%

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

      3. remove-double-neg 52.6%

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

      4. +-commutative 52.6%

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

   3. Simplified 52.6%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. neg-mul-1 99.8%

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

      3. sub-neg 99.8%

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

      4. associate--l+ 99.8%

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

      5. div-sub 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. neg-mul-1 99.8%

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

      9. metadata-eval 99.8%

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

      10. distribute-lft-in 99.8%

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

      11. metadata-eval 99.8%

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

      12. sub-neg 99.8%

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

      13. associate-*r/ 99.8%

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

      14. mul-1-neg 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -250000:\\ \;\;\;\;x + \left(\frac{x + -1}{{y}^{2}} + \frac{1 - x}{y}\right)\\ \mathbf{elif}\;y \leq 7500000:\\ \;\;\;\;1 + \left(x + -1\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{y} + \frac{-1}{{y}^{2}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+21}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.88:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.1e+28)
   x
   (if (<= y -3.6e+21)
     (/ 1.0 y)
     (if (<= y -1.0) x (if (<= y 0.88) (- 1.0 y) x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.1e+28) {
		tmp = x;
	} else if (y <= -3.6e+21) {
		tmp = 1.0 / y;
	} else if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.88) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.1d+28)) then
        tmp = x
    else if (y <= (-3.6d+21)) then
        tmp = 1.0d0 / y
    else if (y <= (-1.0d0)) then
        tmp = x
    else if (y <= 0.88d0) then
        tmp = 1.0d0 - y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.1e+28) {
		tmp = x;
	} else if (y <= -3.6e+21) {
		tmp = 1.0 / y;
	} else if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.88) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.1e+28:
		tmp = x
	elif y <= -3.6e+21:
		tmp = 1.0 / y
	elif y <= -1.0:
		tmp = x
	elif y <= 0.88:
		tmp = 1.0 - y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.1e+28)
		tmp = x;
	elseif (y <= -3.6e+21)
		tmp = Float64(1.0 / y);
	elseif (y <= -1.0)
		tmp = x;
	elseif (y <= 0.88)
		tmp = Float64(1.0 - y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.1e+28)
		tmp = x;
	elseif (y <= -3.6e+21)
		tmp = 1.0 / y;
	elseif (y <= -1.0)
		tmp = x;
	elseif (y <= 0.88)
		tmp = 1.0 - y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.1e+28], x, If[LessEqual[y, -3.6e+21], N[(1.0 / y), $MachinePrecision], If[LessEqual[y, -1.0], x, If[LessEqual[y, 0.88], N[(1.0 - y), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.09999999999999993e28 or -3.6e21 < y < -1 or 0.880000000000000004 < y

   1. Initial program 40.5%

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

      1. associate-/l* 58.1%

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

      2. remove-double-neg 58.1%

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

      3. remove-double-neg 58.1%

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

      4. +-commutative 58.1%

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

   3. Simplified 58.1%

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

   5. Taylor expanded in y around inf 76.3%

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

   if -1.09999999999999993e28 < y < -3.6e21

   1. Initial program 3.3%

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

      1. associate-/l* 3.3%

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

      2. remove-double-neg 3.3%

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

      3. remove-double-neg 3.3%

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

      4. +-commutative 3.3%

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

   3. Simplified 3.3%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

      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. neg-mul-1 100.0%

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

      6. metadata-eval 100.0%

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

      7. distribute-lft-in 100.0%

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

      8. metadata-eval 100.0%

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

      9. sub-neg 100.0%

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

      10. associate-*r/ 100.0%

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

      11. mul-1-neg 100.0%

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

      12. unsub-neg 100.0%

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

      13. sub-neg 100.0%

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

      14. 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%

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

   if -1 < y < 0.880000000000000004

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 76.7%

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

   6. Taylor expanded in y around 0 75.6%

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

      1. neg-mul-1 75.6%

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

      2. unsub-neg 75.6%

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

   8. Simplified 75.6%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+21}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.88:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -120000000:\\ \;\;\;\;x - \frac{x + -1}{y}\\ \mathbf{elif}\;y \leq 13000000000:\\ \;\;\;\;1 + \left(x + -1\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -120000000.0)
   (- x (/ (+ x -1.0) y))
   (if (<= y 13000000000.0)
     (+ 1.0 (* (+ x -1.0) (/ y (+ y 1.0))))
     (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -120000000.0) {
		tmp = x - ((x + -1.0) / y);
	} else if (y <= 13000000000.0) {
		tmp = 1.0 + ((x + -1.0) * (y / (y + 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) :: tmp
    if (y <= (-120000000.0d0)) then
        tmp = x - ((x + (-1.0d0)) / y)
    else if (y <= 13000000000.0d0) then
        tmp = 1.0d0 + ((x + (-1.0d0)) * (y / (y + 1.0d0)))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -120000000.0) {
		tmp = x - ((x + -1.0) / y);
	} else if (y <= 13000000000.0) {
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -120000000.0:
		tmp = x - ((x + -1.0) / y)
	elif y <= 13000000000.0:
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -120000000.0)
		tmp = Float64(x - Float64(Float64(x + -1.0) / y));
	elseif (y <= 13000000000.0)
		tmp = Float64(1.0 + Float64(Float64(x + -1.0) * Float64(y / Float64(y + 1.0))));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -120000000.0)
		tmp = x - ((x + -1.0) / y);
	elseif (y <= 13000000000.0)
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -120000000.0], N[(x - N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 13000000000.0], N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e8

   1. Initial program 36.3%

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

      1. associate-/l* 57.4%

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

      2. remove-double-neg 57.4%

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

      3. remove-double-neg 57.4%

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

      4. +-commutative 57.4%

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

   3. Simplified 57.4%

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

   5. Taylor expanded in y around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. div-sub 99.5%

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

      3. sub-neg 99.5%

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

      4. +-commutative 99.5%

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

      5. neg-mul-1 99.5%

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

      6. metadata-eval 99.5%

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

      7. distribute-lft-in 99.5%

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

      8. metadata-eval 99.5%

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

      9. sub-neg 99.5%

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

      10. associate-*r/ 99.5%

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

      11. mul-1-neg 99.5%

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

      12. unsub-neg 99.5%

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

      13. sub-neg 99.5%

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

      14. metadata-eval 99.5%

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

   7. Simplified 99.5%

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

   if -1.2e8 < y < 1.3e10

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

      2. remove-double-neg 99.6%

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

      3. remove-double-neg 99.6%

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

      4. +-commutative 99.6%

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

   3. Simplified 99.6%

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

   if 1.3e10 < y

   1. Initial program 39.2%

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

      1. associate-/l* 52.3%

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

      2. remove-double-neg 52.3%

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

      3. remove-double-neg 52.3%

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

      4. +-commutative 52.3%

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

   3. Simplified 52.3%

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

   5. Taylor expanded in y around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. div-sub 99.9%

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

      3. sub-neg 99.9%

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

      4. +-commutative 99.9%

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

      5. neg-mul-1 99.9%

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

      6. metadata-eval 99.9%

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

      7. distribute-lft-in 99.9%

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

      8. metadata-eval 99.9%

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

      9. sub-neg 99.9%

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

      10. associate-*r/ 99.9%

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

      11. mul-1-neg 99.9%

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

      12. unsub-neg 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 99.9%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -120000000:\\ \;\;\;\;x - \frac{x + -1}{y}\\ \mathbf{elif}\;y \leq 13000000000:\\ \;\;\;\;1 + \left(x + -1\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.3% accurate, 0.6× speedup

Math

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

FPCore

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

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 * (1.0 - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 0.8d0))) then
        tmp = x + (1.0d0 / y)
    else
        tmp = 1.0d0 - (y * (1.0d0 - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.8)) {
		tmp = x + (1.0 / y);
	} else {
		tmp = 1.0 - (y * (1.0 - x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.8):
		tmp = x + (1.0 / y)
	else:
		tmp = 1.0 - (y * (1.0 - x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.8))
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(1.0 - Float64(y * Float64(1.0 - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.8)))
		tmp = x + (1.0 / y);
	else
		tmp = 1.0 - (y * (1.0 - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.8]], $MachinePrecision]], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.80000000000000004 < y

   1. Initial program 39.1%

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

      1. associate-/l* 56.1%

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

      2. remove-double-neg 56.1%

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

      3. remove-double-neg 56.1%

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

      4. +-commutative 56.1%

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

   3. Simplified 56.1%

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

   5. Taylor expanded in y around inf 98.3%

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

      1. associate--l+ 98.3%

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

      2. div-sub 98.3%

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

      3. sub-neg 98.3%

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

      4. +-commutative 98.3%

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

      5. neg-mul-1 98.3%

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

      6. metadata-eval 98.3%

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

      7. distribute-lft-in 98.3%

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

      8. metadata-eval 98.3%

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

      9. sub-neg 98.3%

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

      10. associate-*r/ 98.3%

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

      11. mul-1-neg 98.3%

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

      12. unsub-neg 98.3%

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

      13. sub-neg 98.3%

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

      14. metadata-eval 98.3%

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

   7. Simplified 98.3%

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

   8. Taylor expanded in x around 0 97.9%

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

   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. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.9%

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

4. Final simplification 98.4%

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

Alternative 7: 98.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 39.1%

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

      1. associate-/l* 56.1%

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

      2. remove-double-neg 56.1%

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

      3. remove-double-neg 56.1%

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

      4. +-commutative 56.1%

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

   3. Simplified 56.1%

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

   5. Taylor expanded in y around inf 98.3%

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

      1. associate--l+ 98.3%

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

      2. div-sub 98.3%

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

      3. sub-neg 98.3%

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

      4. +-commutative 98.3%

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

      5. neg-mul-1 98.3%

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

      6. metadata-eval 98.3%

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

      7. distribute-lft-in 98.3%

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

      8. metadata-eval 98.3%

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

      9. sub-neg 98.3%

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

      10. associate-*r/ 98.3%

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

      11. mul-1-neg 98.3%

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

      12. unsub-neg 98.3%

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

      13. sub-neg 98.3%

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

      14. metadata-eval 98.3%

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

   7. Simplified 98.3%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.9%

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

4. Final simplification 98.6%

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

Alternative 8: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.102\right):\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.102))) (+ x (/ 1.0 y)) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.102)) {
		tmp = x + (1.0 / y);
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 0.102d0))) then
        tmp = x + (1.0d0 / y)
    else
        tmp = 1.0d0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.102)) {
		tmp = x + (1.0 / y);
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.102):
		tmp = x + (1.0 / y)
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.102))
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(1.0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.102)))
		tmp = x + (1.0 / y);
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.102]], $MachinePrecision]], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.101999999999999993 < y

   1. Initial program 39.1%

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

      1. associate-/l* 56.1%

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

      2. remove-double-neg 56.1%

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

      3. remove-double-neg 56.1%

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

      4. +-commutative 56.1%

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

   3. Simplified 56.1%

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

   5. Taylor expanded in y around inf 98.3%

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

      1. associate--l+ 98.3%

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

      2. div-sub 98.3%

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

      3. sub-neg 98.3%

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

      4. +-commutative 98.3%

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

      5. neg-mul-1 98.3%

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

      6. metadata-eval 98.3%

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

      7. distribute-lft-in 98.3%

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

      8. metadata-eval 98.3%

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

      9. sub-neg 98.3%

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

      10. associate-*r/ 98.3%

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

      11. mul-1-neg 98.3%

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

      12. unsub-neg 98.3%

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

      13. sub-neg 98.3%

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

      14. metadata-eval 98.3%

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

   7. Simplified 98.3%

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

   8. Taylor expanded in x around 0 97.9%

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

   if -1 < y < 0.101999999999999993

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 76.7%

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

   6. Taylor expanded in y around 0 75.6%

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

      1. neg-mul-1 75.6%

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

      2. unsub-neg 75.6%

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

   8. Simplified 75.6%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.102\right):\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.1% 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 39.1%

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

      1. associate-/l* 56.1%

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

      2. remove-double-neg 56.1%

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

      3. remove-double-neg 56.1%

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

      4. +-commutative 56.1%

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

   3. Simplified 56.1%

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

   5. Taylor expanded in y around inf 98.3%

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

      1. associate--l+ 98.3%

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

      2. div-sub 98.3%

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

      3. sub-neg 98.3%

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

      4. +-commutative 98.3%

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

      5. neg-mul-1 98.3%

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

      6. metadata-eval 98.3%

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

      7. distribute-lft-in 98.3%

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

      8. metadata-eval 98.3%

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

      9. sub-neg 98.3%

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

      10. associate-*r/ 98.3%

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

      11. mul-1-neg 98.3%

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

      12. unsub-neg 98.3%

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

      13. sub-neg 98.3%

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

      14. metadata-eval 98.3%

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

   7. Simplified 98.3%

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

   8. Taylor expanded in x around 0 97.9%

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

   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. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.9%

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

   6. Taylor expanded in x around inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. distribute-lft-neg-out 97.9%

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

      3. *-commutative 97.9%

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

   8. Simplified 97.9%

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

4. Final simplification 97.9%

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

Alternative 10: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.72:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 0.72) (- 1.0 y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.72) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = x
    else if (y <= 0.72d0) then
        tmp = 1.0d0 - y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.72) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.72:
		tmp = 1.0 - y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.72)
		tmp = Float64(1.0 - y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.72)
		tmp = 1.0 - y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 0.72], N[(1.0 - y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.71999999999999997 < y

   1. Initial program 39.1%

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

      1. associate-/l* 56.1%

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

      2. remove-double-neg 56.1%

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

      3. remove-double-neg 56.1%

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

      4. +-commutative 56.1%

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

   3. Simplified 56.1%

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

   5. Taylor expanded in y around inf 73.5%

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

   if -1 < y < 0.71999999999999997

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 76.7%

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

   6. Taylor expanded in y around 0 75.6%

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

      1. neg-mul-1 75.6%

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

      2. unsub-neg 75.6%

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

   8. Simplified 75.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.72:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.92:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 0.92) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.92) {
		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 <= 0.92d0) 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 <= 0.92) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.92:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.92)
		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 <= 0.92)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 0.92], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.92000000000000004 < y

   1. Initial program 39.1%

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

      1. associate-/l* 56.1%

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

      2. remove-double-neg 56.1%

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

      3. remove-double-neg 56.1%

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

      4. +-commutative 56.1%

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

   3. Simplified 56.1%

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

   5. Taylor expanded in y around inf 73.5%

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

   if -1 < y < 0.92000000000000004

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 74.6%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.92:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.9% 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 68.4%

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

   1. associate-/l* 77.2%

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

   2. remove-double-neg 77.2%

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

   3. remove-double-neg 77.2%

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

   4. +-commutative 77.2%

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

3. Simplified 77.2%

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

5. Taylor expanded in y around 0 37.9%

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

6. Final simplification 37.9%

   \[\leadsto 1 \]
7. Add Preprocessing

Developer target: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \mathbf{if}\;y < -3693.8482788297247:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 6799310503.41891:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024041 
(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))))