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

Percentage Accurate: 65.7% → 99.9%

Time: 9.5s

Alternatives: 13

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: 65.7% 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, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{1 + y}\\ \mathbf{if}\;t\_0 \leq 0.8:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;x + \frac{1 + \left(\frac{\left(x + -1\right) + \frac{1 - x}{y}}{y} - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{1 + y} + \frac{y - \left(1 + y\right)}{x \cdot \left(-1 - y\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (- 1.0 x) y) (+ 1.0 y))))
   (if (<= t_0 0.8)
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (if (<= t_0 1.0)
       (+ x (/ (+ 1.0 (- (/ (+ (+ x -1.0) (/ (- 1.0 x) y)) y) x)) y))
       (* x (+ (/ y (+ 1.0 y)) (/ (- y (+ 1.0 y)) (* 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 <= 0.8) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else if (t_0 <= 1.0) {
		tmp = x + ((1.0 + ((((x + -1.0) + ((1.0 - x) / y)) / y) - x)) / y);
	} else {
		tmp = x * ((y / (1.0 + y)) + ((y - (1.0 + y)) / (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 <= 0.8d0) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else if (t_0 <= 1.0d0) then
        tmp = x + ((1.0d0 + ((((x + (-1.0d0)) + ((1.0d0 - x) / y)) / y) - x)) / y)
    else
        tmp = x * ((y / (1.0d0 + y)) + ((y - (1.0d0 + y)) / (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 <= 0.8) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else if (t_0 <= 1.0) {
		tmp = x + ((1.0 + ((((x + -1.0) + ((1.0 - x) / y)) / y) - x)) / y);
	} else {
		tmp = x * ((y / (1.0 + y)) + ((y - (1.0 + y)) / (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 <= 0.8:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	elif t_0 <= 1.0:
		tmp = x + ((1.0 + ((((x + -1.0) + ((1.0 - x) / y)) / y) - x)) / y)
	else:
		tmp = x * ((y / (1.0 + y)) + ((y - (1.0 + y)) / (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 <= 0.8)
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	elseif (t_0 <= 1.0)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(Float64(Float64(Float64(x + -1.0) + Float64(Float64(1.0 - x) / y)) / y) - x)) / y));
	else
		tmp = Float64(x * Float64(Float64(y / Float64(1.0 + y)) + Float64(Float64(y - Float64(1.0 + y)) / 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 <= 0.8)
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	elseif (t_0 <= 1.0)
		tmp = x + ((1.0 + ((((x + -1.0) + ((1.0 - x) / y)) / y) - x)) / y);
	else
		tmp = x * ((y / (1.0 + y)) + ((y - (1.0 + y)) / (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[LessEqual[t$95$0, 0.8], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1.0], N[(x + N[(N[(1.0 + N[(N[(N[(N[(x + -1.0), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y - N[(1.0 + y), $MachinePrecision]), $MachinePrecision] / N[(x * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.80000000000000004

   1. Initial program 89.1%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   if 0.80000000000000004 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1

   1. Initial program 6.4%

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

      1. associate-/l* 6.4%

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

      2. remove-double-neg 6.4%

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

      3. remove-double-neg 6.4%

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

      4. +-commutative 6.4%

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

   3. Simplified 6.4%

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

   5. Taylor expanded in y around -inf 99.9%

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

   7. Simplified 99.9%

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

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

   1. Initial program 61.0%

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

      1. associate-/l* 96.3%

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

      2. remove-double-neg 96.3%

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

      3. remove-double-neg 96.3%

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

      4. +-commutative 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around inf 99.2%

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

      1. associate--r+ 99.2%

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

      2. cancel-sign-sub-inv 99.2%

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

      3. metadata-eval 99.2%

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

      4. *-lft-identity 99.2%

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

      5. unsub-neg 99.2%

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

      6. +-commutative 99.2%

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

      7. mul-1-neg 99.2%

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

      8. associate-+l+ 99.2%

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

      9. mul-1-neg 99.2%

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

      10. associate-/r* 99.2%

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

      11. distribute-neg-frac2 99.2%

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

      12. distribute-neg-in 99.2%

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

      13. metadata-eval 99.2%

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

      14. sub-neg 99.2%

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

   7. Simplified 99.2%

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

      1. frac-add 100.0%

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

      2. div-inv 100.0%

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

      3. *-un-lft-identity 100.0%

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

      4. clear-num 100.0%

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

      5. un-div-inv 98.8%

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

   9. Applied egg-rr 98.8%

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

       1. associate-*r/ 98.8%

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

       2. *-rgt-identity 98.8%

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

       3. +-commutative 98.8%

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

       4. associate-/r/ 100.0%

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

       5. *-inverses 100.0%

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

       6. *-lft-identity 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 99.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{1 + y}\\ \mathbf{if}\;t\_0 \leq 0.8:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{1 + y} + \frac{y - \left(1 + y\right)}{x \cdot \left(-1 - y\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (- 1.0 x) y) (+ 1.0 y))))
   (if (<= t_0 0.8)
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (if (<= t_0 1.0)
       (+ x (/ (+ (- 1.0 x) (/ (+ x -1.0) y)) y))
       (* x (+ (/ y (+ 1.0 y)) (/ (- y (+ 1.0 y)) (* 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 <= 0.8) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else if (t_0 <= 1.0) {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	} else {
		tmp = x * ((y / (1.0 + y)) + ((y - (1.0 + y)) / (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 <= 0.8d0) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else if (t_0 <= 1.0d0) then
        tmp = x + (((1.0d0 - x) + ((x + (-1.0d0)) / y)) / y)
    else
        tmp = x * ((y / (1.0d0 + y)) + ((y - (1.0d0 + y)) / (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 <= 0.8) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else if (t_0 <= 1.0) {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	} else {
		tmp = x * ((y / (1.0 + y)) + ((y - (1.0 + y)) / (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 <= 0.8:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	elif t_0 <= 1.0:
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y)
	else:
		tmp = x * ((y / (1.0 + y)) + ((y - (1.0 + y)) / (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 <= 0.8)
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	elseif (t_0 <= 1.0)
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(x + -1.0) / y)) / y));
	else
		tmp = Float64(x * Float64(Float64(y / Float64(1.0 + y)) + Float64(Float64(y - Float64(1.0 + y)) / 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 <= 0.8)
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	elseif (t_0 <= 1.0)
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	else
		tmp = x * ((y / (1.0 + y)) + ((y - (1.0 + y)) / (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[LessEqual[t$95$0, 0.8], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1.0], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y - N[(1.0 + y), $MachinePrecision]), $MachinePrecision] / N[(x * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.80000000000000004

   1. Initial program 89.1%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   if 0.80000000000000004 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1

   1. Initial program 6.4%

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

      1. associate-/l* 6.4%

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

      2. remove-double-neg 6.4%

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

      3. remove-double-neg 6.4%

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

      4. +-commutative 6.4%

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

   3. Simplified 6.4%

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

   5. Taylor expanded in y around -inf 99.7%

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

   7. Simplified 99.7%

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

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

   1. Initial program 61.0%

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

      1. associate-/l* 96.3%

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

      2. remove-double-neg 96.3%

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

      3. remove-double-neg 96.3%

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

      4. +-commutative 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around inf 99.2%

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

      1. associate--r+ 99.2%

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

      2. cancel-sign-sub-inv 99.2%

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

      3. metadata-eval 99.2%

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

      4. *-lft-identity 99.2%

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

      5. unsub-neg 99.2%

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

      6. +-commutative 99.2%

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

      7. mul-1-neg 99.2%

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

      8. associate-+l+ 99.2%

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

      9. mul-1-neg 99.2%

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

      10. associate-/r* 99.2%

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

      11. distribute-neg-frac2 99.2%

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

      12. distribute-neg-in 99.2%

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

      13. metadata-eval 99.2%

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

      14. sub-neg 99.2%

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

   7. Simplified 99.2%

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

      1. frac-add 100.0%

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

      2. div-inv 100.0%

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

      3. *-un-lft-identity 100.0%

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

      4. clear-num 100.0%

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

      5. un-div-inv 98.8%

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

   9. Applied egg-rr 98.8%

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

       1. associate-*r/ 98.8%

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

       2. *-rgt-identity 98.8%

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

       3. +-commutative 98.8%

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

       4. associate-/r/ 100.0%

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

       5. *-inverses 100.0%

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

       6. *-lft-identity 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 99.9%

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

Alternative 3: 99.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{1 + y}\\ \mathbf{if}\;t\_0 \leq 0.8:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{1 + y} + \left(\frac{1}{x} + \frac{\frac{y}{x}}{-1 - y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (- 1.0 x) y) (+ 1.0 y))))
   (if (<= t_0 0.8)
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (if (<= t_0 1.0)
       (+ x (/ (+ (- 1.0 x) (/ (+ x -1.0) y)) y))
       (* x (+ (/ y (+ 1.0 y)) (+ (/ 1.0 x) (/ (/ y 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 <= 0.8) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else if (t_0 <= 1.0) {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	} else {
		tmp = x * ((y / (1.0 + y)) + ((1.0 / x) + ((y / 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 <= 0.8d0) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else if (t_0 <= 1.0d0) then
        tmp = x + (((1.0d0 - x) + ((x + (-1.0d0)) / y)) / y)
    else
        tmp = x * ((y / (1.0d0 + y)) + ((1.0d0 / x) + ((y / 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 <= 0.8) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else if (t_0 <= 1.0) {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	} else {
		tmp = x * ((y / (1.0 + y)) + ((1.0 / x) + ((y / 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 <= 0.8:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	elif t_0 <= 1.0:
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y)
	else:
		tmp = x * ((y / (1.0 + y)) + ((1.0 / x) + ((y / 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 <= 0.8)
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	elseif (t_0 <= 1.0)
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(x + -1.0) / y)) / y));
	else
		tmp = Float64(x * Float64(Float64(y / Float64(1.0 + y)) + Float64(Float64(1.0 / x) + Float64(Float64(y / 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 <= 0.8)
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	elseif (t_0 <= 1.0)
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	else
		tmp = x * ((y / (1.0 + y)) + ((1.0 / x) + ((y / 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[LessEqual[t$95$0, 0.8], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1.0], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x), $MachinePrecision] + N[(N[(y / x), $MachinePrecision] / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.80000000000000004

   1. Initial program 89.1%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   if 0.80000000000000004 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1

   1. Initial program 6.4%

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

      1. associate-/l* 6.4%

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

      2. remove-double-neg 6.4%

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

      3. remove-double-neg 6.4%

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

      4. +-commutative 6.4%

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

   3. Simplified 6.4%

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

   5. Taylor expanded in y around -inf 99.7%

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

   7. Simplified 99.7%

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

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

   1. Initial program 61.0%

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

      1. associate-/l* 96.3%

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

      2. remove-double-neg 96.3%

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

      3. remove-double-neg 96.3%

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

      4. +-commutative 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around inf 99.2%

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

      1. associate--r+ 99.2%

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

      2. cancel-sign-sub-inv 99.2%

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

      3. metadata-eval 99.2%

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

      4. *-lft-identity 99.2%

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

      5. unsub-neg 99.2%

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

      6. +-commutative 99.2%

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

      7. mul-1-neg 99.2%

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

      8. associate-+l+ 99.2%

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

      9. mul-1-neg 99.2%

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

      10. associate-/r* 99.2%

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

      11. distribute-neg-frac2 99.2%

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

      12. distribute-neg-in 99.2%

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

      13. metadata-eval 99.2%

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

      14. sub-neg 99.2%

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

   7. Simplified 99.2%

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

4. Final simplification 99.8%

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

Alternative 4: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{1 + y}\\ \mathbf{if}\;t\_0 \leq 0.8 \lor \neg \left(t\_0 \leq 1.000005\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (- 1.0 x) y) (+ 1.0 y))))
   (if (or (<= t_0 0.8) (not (<= t_0 1.000005)))
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (+ x (/ (+ (- 1.0 x) (/ (+ x -1.0) y)) y)))))

C

double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double tmp;
	if ((t_0 <= 0.8) || !(t_0 <= 1.000005)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / 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 <= 0.8d0) .or. (.not. (t_0 <= 1.000005d0))) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else
        tmp = x + (((1.0d0 - x) + ((x + (-1.0d0)) / y)) / 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 <= 0.8) || !(t_0 <= 1.000005)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((1.0 - x) * y) / (1.0 + y)
	tmp = 0
	if (t_0 <= 0.8) or not (t_0 <= 1.000005):
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	else:
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / 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 <= 0.8) || !(t_0 <= 1.000005))
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	else
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(x + -1.0) / y)) / 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 <= 0.8) || ~((t_0 <= 1.000005)))
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	else
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / 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, 0.8], N[Not[LessEqual[t$95$0, 1.000005]], $MachinePrecision]], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.80000000000000004 or 1.00000500000000003 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 82.4%

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

      1. associate-/l* 99.8%

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

      2. remove-double-neg 99.8%

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

      3. remove-double-neg 99.8%

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

      4. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   if 0.80000000000000004 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1.00000500000000003

   1. Initial program 8.6%

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

      1. associate-/l* 8.6%

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

      2. remove-double-neg 8.6%

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

      3. remove-double-neg 8.6%

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

      4. +-commutative 8.6%

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

   3. Simplified 8.6%

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

   5. Taylor expanded in y around -inf 99.7%

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

   7. Simplified 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 0.8 \lor \neg \left(\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 1.000005\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{1 + y}\\ \mathbf{if}\;t\_0 \leq 1 \lor \neg \left(t\_0 \leq 1.000005\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (- 1.0 x) y) (+ 1.0 y))))
   (if (or (<= t_0 1.0) (not (<= t_0 1.000005)))
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (+ 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 <= 1.0) || !(t_0 <= 1.000005)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} 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 <= 1.0d0) .or. (.not. (t_0 <= 1.000005d0))) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    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 <= 1.0) || !(t_0 <= 1.000005)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} 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 <= 1.0) or not (t_0 <= 1.000005):
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	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 <= 1.0) || !(t_0 <= 1.000005))
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	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 <= 1.0) || ~((t_0 <= 1.000005)))
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	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, 1.0], N[Not[LessEqual[t$95$0, 1.000005]], $MachinePrecision]], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1 or 1.00000500000000003 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 64.7%

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

      1. associate-/l* 78.0%

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

      2. remove-double-neg 78.0%

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

      3. remove-double-neg 78.0%

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

      4. +-commutative 78.0%

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

   3. Simplified 78.0%

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

   if 1 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1.00000500000000003

   1. Initial program 51.8%

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

      1. associate-/l* 51.8%

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

      2. remove-double-neg 51.8%

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

      3. remove-double-neg 51.8%

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

      4. +-commutative 51.8%

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

   3. Simplified 51.8%

      \[\leadsto \color{blue}{1 - \left(1 - x\right) \cdot \frac{y}{1 + y}} \]
   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-sub0 100.0%

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

      6. associate-+l- 100.0%

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

      7. neg-sub0 100.0%

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

      8. mul-1-neg 100.0%

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

      9. associate-*r/ 100.0%

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

      10. mul-1-neg 100.0%

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

      11. unsub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 1 \lor \neg \left(\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 1.000005\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9:\\ \;\;\;\;1 + x \cdot y\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+103}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y 1.9) (+ 1.0 (* x y)) (if (<= y 5.6e+103) (/ 1.0 y) x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 1.9) {
		tmp = 1.0 + (x * y);
	} else if (y <= 5.6e+103) {
		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 <= 1.9d0) then
        tmp = 1.0d0 + (x * y)
    else if (y <= 5.6d+103) 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 <= 1.9) {
		tmp = 1.0 + (x * y);
	} else if (y <= 5.6e+103) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 1.9:
		tmp = 1.0 + (x * y)
	elif y <= 5.6e+103:
		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 <= 1.9)
		tmp = Float64(1.0 + Float64(x * y));
	elseif (y <= 5.6e+103)
		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 <= 1.9)
		tmp = 1.0 + (x * y);
	elseif (y <= 5.6e+103)
		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, 1.9], N[(1.0 + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+103], N[(1.0 / y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 5.60000000000000017e103 < y

   1. Initial program 24.0%

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

      1. associate-/l* 57.8%

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

      2. remove-double-neg 57.8%

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

      3. remove-double-neg 57.8%

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

      4. +-commutative 57.8%

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

   3. Simplified 57.8%

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

   5. Taylor expanded in y around inf 82.3%

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

   if -1 < y < 1.8999999999999999

   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%

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

   6. Taylor expanded in x around inf 98.4%

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

      1. mul-1-neg 98.4%

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

      2. distribute-lft-neg-out 98.4%

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

      3. *-commutative 98.4%

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

   8. Simplified 98.4%

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

      1. sub-neg 98.4%

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

      2. distribute-rgt-neg-out 98.4%

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

      3. remove-double-neg 98.4%

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

      4. +-commutative 98.4%

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

   10. Applied egg-rr 98.4%

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

   if 1.8999999999999999 < y < 5.60000000000000017e103

   1. Initial program 28.9%

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

      1. associate-/l* 32.8%

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

      2. remove-double-neg 32.8%

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

      3. remove-double-neg 32.8%

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

      4. +-commutative 32.8%

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

   3. Simplified 32.8%

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

   5. Taylor expanded in y around inf 92.8%

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

      1. associate--l+ 92.8%

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

      2. div-sub 92.8%

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

      3. sub-neg 92.8%

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

      4. +-commutative 92.8%

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

      5. neg-sub0 92.8%

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

      6. associate-+l- 92.8%

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

      7. neg-sub0 92.8%

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

      8. mul-1-neg 92.8%

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

      9. associate-*r/ 92.8%

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

      10. mul-1-neg 92.8%

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

      11. unsub-neg 92.8%

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

      12. sub-neg 92.8%

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

      13. metadata-eval 92.8%

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

   7. Simplified 92.8%

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

   8. Taylor expanded in x around 0 67.4%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9:\\ \;\;\;\;1 + x \cdot y\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+103}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.75:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+103}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y 0.75) (- 1.0 y) (if (<= y 5.6e+103) (/ 1.0 y) x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.75) {
		tmp = 1.0 - y;
	} else if (y <= 5.6e+103) {
		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 <= 0.75d0) then
        tmp = 1.0d0 - y
    else if (y <= 5.6d+103) 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 <= 0.75) {
		tmp = 1.0 - y;
	} else if (y <= 5.6e+103) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.75:
		tmp = 1.0 - y
	elif y <= 5.6e+103:
		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 <= 0.75)
		tmp = Float64(1.0 - y);
	elseif (y <= 5.6e+103)
		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 <= 0.75)
		tmp = 1.0 - y;
	elseif (y <= 5.6e+103)
		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, 0.75], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, 5.6e+103], N[(1.0 / y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 5.60000000000000017e103 < y

   1. Initial program 24.0%

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

      1. associate-/l* 57.8%

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

      2. remove-double-neg 57.8%

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

      3. remove-double-neg 57.8%

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

      4. +-commutative 57.8%

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

   3. Simplified 57.8%

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

   5. Taylor expanded in y around inf 82.3%

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

   if -1 < y < 0.75

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. fma-define 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

      11. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 78.0%

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

      1. metadata-eval 78.0%

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

      2. distribute-neg-frac 78.0%

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

      3. distribute-frac-neg2 78.0%

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

      4. distribute-neg-in 78.0%

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

      5. metadata-eval 78.0%

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

      6. sub-neg 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in y around 0 77.9%

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

      1. neg-mul-1 77.9%

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

      2. unsub-neg 77.9%

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

   10. Simplified 77.9%

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

   if 0.75 < y < 5.60000000000000017e103

   1. Initial program 28.9%

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

      1. associate-/l* 32.8%

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

      2. remove-double-neg 32.8%

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

      3. remove-double-neg 32.8%

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

      4. +-commutative 32.8%

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

   3. Simplified 32.8%

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

   5. Taylor expanded in y around inf 92.8%

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

      1. associate--l+ 92.8%

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

      2. div-sub 92.8%

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

      3. sub-neg 92.8%

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

      4. +-commutative 92.8%

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

      5. neg-sub0 92.8%

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

      6. associate-+l- 92.8%

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

      7. neg-sub0 92.8%

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

      8. mul-1-neg 92.8%

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

      9. associate-*r/ 92.8%

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

      10. mul-1-neg 92.8%

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

      11. unsub-neg 92.8%

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

      12. sub-neg 92.8%

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

      13. metadata-eval 92.8%

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

   7. Simplified 92.8%

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

   8. Taylor expanded in x around 0 67.4%

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

Alternative 8: 98.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 25.0%

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

      1. associate-/l* 52.8%

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

      2. remove-double-neg 52.8%

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

      3. remove-double-neg 52.8%

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

      4. +-commutative 52.8%

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

   3. Simplified 52.8%

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

   5. Taylor expanded in y around inf 97.5%

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

      1. associate--l+ 97.5%

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

      2. div-sub 97.5%

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

      3. sub-neg 97.5%

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

      4. +-commutative 97.5%

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

      5. neg-sub0 97.5%

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

      6. associate-+l- 97.5%

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

      7. neg-sub0 97.5%

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

      8. mul-1-neg 97.5%

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

      9. associate-*r/ 97.5%

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

      10. mul-1-neg 97.5%

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

      11. unsub-neg 97.5%

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

      12. sub-neg 97.5%

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

      13. metadata-eval 97.5%

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

   7. Simplified 97.5%

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

   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%

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

4. Final simplification 98.3%

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

Alternative 9: 97.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.78000000000000003 < y

   1. Initial program 25.0%

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

      1. associate-/l* 52.8%

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

      2. remove-double-neg 52.8%

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

      3. remove-double-neg 52.8%

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

      4. +-commutative 52.8%

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

   3. Simplified 52.8%

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

   5. Taylor expanded in y around inf 97.5%

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

      1. associate--l+ 97.5%

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

      2. div-sub 97.5%

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

      3. sub-neg 97.5%

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

      4. +-commutative 97.5%

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

      5. neg-sub0 97.5%

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

      6. associate-+l- 97.5%

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

      7. neg-sub0 97.5%

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

      8. mul-1-neg 97.5%

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

      9. associate-*r/ 97.5%

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

      10. mul-1-neg 97.5%

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

      11. unsub-neg 97.5%

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

      12. sub-neg 97.5%

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

      13. metadata-eval 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in x around 0 97.0%

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

   if -1 < y < 0.78000000000000003

   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%

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

4. Final simplification 98.0%

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

Alternative 10: 97.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 25.0%

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

      1. associate-/l* 52.8%

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

      2. remove-double-neg 52.8%

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

      3. remove-double-neg 52.8%

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

      4. +-commutative 52.8%

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

   3. Simplified 52.8%

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

   5. Taylor expanded in y around inf 97.5%

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

      1. associate--l+ 97.5%

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

      2. div-sub 97.5%

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

      3. sub-neg 97.5%

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

      4. +-commutative 97.5%

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

      5. neg-sub0 97.5%

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

      6. associate-+l- 97.5%

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

      7. neg-sub0 97.5%

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

      8. mul-1-neg 97.5%

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

      9. associate-*r/ 97.5%

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

      10. mul-1-neg 97.5%

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

      11. unsub-neg 97.5%

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

      12. sub-neg 97.5%

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

      13. metadata-eval 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in x around 0 97.0%

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

   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%

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

   6. Taylor expanded in x around inf 98.4%

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

      1. mul-1-neg 98.4%

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

      2. distribute-lft-neg-out 98.4%

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

      3. *-commutative 98.4%

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

   8. Simplified 98.4%

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

      1. sub-neg 98.4%

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

      2. distribute-rgt-neg-out 98.4%

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

      3. remove-double-neg 98.4%

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

      4. +-commutative 98.4%

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

   10. Applied egg-rr 98.4%

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

4. Final simplification 97.7%

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

Alternative 11: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.0019:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 0.0019) (- 1.0 y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.0019) {
		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 <= 0.0019d0) 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 <= 0.0019) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.0019:
		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 <= 0.0019)
		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 <= 0.0019)
		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, 0.0019], N[(1.0 - y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.0019 < y

   1. Initial program 25.6%

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

      1. associate-/l* 53.2%

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

      2. remove-double-neg 53.2%

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

      3. remove-double-neg 53.2%

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

      4. +-commutative 53.2%

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

   3. Simplified 53.2%

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

   5. Taylor expanded in y around inf 70.2%

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

   if -1 < y < 0.0019

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. fma-define 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

      11. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 78.5%

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

      1. metadata-eval 78.5%

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

      2. distribute-neg-frac 78.5%

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

      3. distribute-frac-neg2 78.5%

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

      4. distribute-neg-in 78.5%

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

      5. metadata-eval 78.5%

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

      6. sub-neg 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in y around 0 78.4%

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

      1. neg-mul-1 78.4%

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

      2. unsub-neg 78.4%

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

   10. Simplified 78.4%

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

Alternative 12: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 30500000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 30500000.0) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 30500000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = x
    else if (y <= 30500000.0d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 30500000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 30500000.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 30500000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 30500000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 30500000.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 3.05e7 < y

   1. Initial program 23.7%

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

      1. associate-/l* 52.2%

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

      2. remove-double-neg 52.2%

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

      3. remove-double-neg 52.2%

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

      4. +-commutative 52.2%

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

   3. Simplified 52.2%

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

   5. Taylor expanded in y around inf 72.5%

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

   if -1 < y < 3.05e7

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

      2. remove-double-neg 99.5%

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

      3. remove-double-neg 99.5%

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

      4. +-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 76.0%

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

Alternative 13: 37.8% 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 64.5%

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

   1. associate-/l* 77.7%

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

   2. remove-double-neg 77.7%

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

   3. remove-double-neg 77.7%

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

   4. +-commutative 77.7%

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

3. Simplified 77.7%

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

5. Taylor expanded in y around 0 42.6%

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

Developer Target 1: 99.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024113 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

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

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