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

Percentage Accurate: 100.0% → 100.0%

Time: 7.4s

Alternatives: 11

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{1 - y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{1 - y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{1 - y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{1 - y} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 98.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{1 - y}\\ t_1 := \frac{x}{1 - y}\\ \mathbf{if}\;t\_0 \leq -100000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\left(-1 - y\right) \cdot \left(y - x\right)\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- 1.0 y))) (t_1 (/ x (- 1.0 y))))
   (if (<= t_0 -100000.0)
     t_1
     (if (<= t_0 5e-10)
       (* (- -1.0 y) (- y x))
       (if (<= t_0 2.0) (/ y (+ y -1.0)) t_1)))))

C

double code(double x, double y) {
	double t_0 = (x - y) / (1.0 - y);
	double t_1 = x / (1.0 - y);
	double tmp;
	if (t_0 <= -100000.0) {
		tmp = t_1;
	} else if (t_0 <= 5e-10) {
		tmp = (-1.0 - y) * (y - x);
	} else if (t_0 <= 2.0) {
		tmp = y / (y + -1.0);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (x - y) / (1.0d0 - y)
    t_1 = x / (1.0d0 - y)
    if (t_0 <= (-100000.0d0)) then
        tmp = t_1
    else if (t_0 <= 5d-10) then
        tmp = ((-1.0d0) - y) * (y - x)
    else if (t_0 <= 2.0d0) then
        tmp = y / (y + (-1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) / (1.0 - y);
	double t_1 = x / (1.0 - y);
	double tmp;
	if (t_0 <= -100000.0) {
		tmp = t_1;
	} else if (t_0 <= 5e-10) {
		tmp = (-1.0 - y) * (y - x);
	} else if (t_0 <= 2.0) {
		tmp = y / (y + -1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / (1.0 - y)
	t_1 = x / (1.0 - y)
	tmp = 0
	if t_0 <= -100000.0:
		tmp = t_1
	elif t_0 <= 5e-10:
		tmp = (-1.0 - y) * (y - x)
	elif t_0 <= 2.0:
		tmp = y / (y + -1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(1.0 - y))
	t_1 = Float64(x / Float64(1.0 - y))
	tmp = 0.0
	if (t_0 <= -100000.0)
		tmp = t_1;
	elseif (t_0 <= 5e-10)
		tmp = Float64(Float64(-1.0 - y) * Float64(y - x));
	elseif (t_0 <= 2.0)
		tmp = Float64(y / Float64(y + -1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / (1.0 - y);
	t_1 = x / (1.0 - y);
	tmp = 0.0;
	if (t_0 <= -100000.0)
		tmp = t_1;
	elseif (t_0 <= 5e-10)
		tmp = (-1.0 - y) * (y - x);
	elseif (t_0 <= 2.0)
		tmp = y / (y + -1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -100000.0], t$95$1, If[LessEqual[t$95$0, 5e-10], N[(N[(-1.0 - y), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2.0], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 1 binary64) y)) < -1e5 or 2 < (/.f64 (-.f64 x y) (-.f64 #s(literal 1 binary64) y))

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 98.0

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

   5. Simplified 98.0%

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

   if -1e5 < (/.f64 (-.f64 x y) (-.f64 #s(literal 1 binary64) y)) < 5.00000000000000031e-10

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

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

      2. frac-2neg N/A

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

      3. associate-/r/ N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. neg-sub0 N/A

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

      7. associate--r- N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. +-lowering-+.f64 N/A

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

      11. neg-sub0 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate--r+ N/A

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

      15. neg-sub0 N/A

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

      16. remove-double-neg N/A

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

      17. --lowering--.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 99.2

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

   7. Simplified 99.2%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 #s(literal 1 binary64) y)) < 2

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. neg-sub0 N/A

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

      5. associate--r- N/A

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

      6. metadata-eval N/A

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

      7. +-lowering-+.f64 99.0

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

   5. Simplified 99.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{1 - y} \leq -100000:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;\frac{x - y}{1 - y} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\left(-1 - y\right) \cdot \left(y - x\right)\\ \mathbf{elif}\;\frac{x - y}{1 - y} \leq 2:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{1 - y}\\ t_1 := \frac{x}{1 - y}\\ \mathbf{if}\;t\_0 \leq -100000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.4:\\ \;\;\;\;\left(-1 - y\right) \cdot \left(y - x\right)\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- 1.0 y))) (t_1 (/ x (- 1.0 y))))
   (if (<= t_0 -100000.0)
     t_1
     (if (<= t_0 0.4) (* (- -1.0 y) (- y x)) (if (<= t_0 2.0) 1.0 t_1)))))

C

double code(double x, double y) {
	double t_0 = (x - y) / (1.0 - y);
	double t_1 = x / (1.0 - y);
	double tmp;
	if (t_0 <= -100000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.4) {
		tmp = (-1.0 - y) * (y - x);
	} else if (t_0 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (x - y) / (1.0d0 - y)
    t_1 = x / (1.0d0 - y)
    if (t_0 <= (-100000.0d0)) then
        tmp = t_1
    else if (t_0 <= 0.4d0) then
        tmp = ((-1.0d0) - y) * (y - x)
    else if (t_0 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) / (1.0 - y);
	double t_1 = x / (1.0 - y);
	double tmp;
	if (t_0 <= -100000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.4) {
		tmp = (-1.0 - y) * (y - x);
	} else if (t_0 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / (1.0 - y)
	t_1 = x / (1.0 - y)
	tmp = 0
	if t_0 <= -100000.0:
		tmp = t_1
	elif t_0 <= 0.4:
		tmp = (-1.0 - y) * (y - x)
	elif t_0 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(1.0 - y))
	t_1 = Float64(x / Float64(1.0 - y))
	tmp = 0.0
	if (t_0 <= -100000.0)
		tmp = t_1;
	elseif (t_0 <= 0.4)
		tmp = Float64(Float64(-1.0 - y) * Float64(y - x));
	elseif (t_0 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / (1.0 - y);
	t_1 = x / (1.0 - y);
	tmp = 0.0;
	if (t_0 <= -100000.0)
		tmp = t_1;
	elseif (t_0 <= 0.4)
		tmp = (-1.0 - y) * (y - x);
	elseif (t_0 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -100000.0], t$95$1, If[LessEqual[t$95$0, 0.4], N[(N[(-1.0 - y), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2.0], 1.0, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 1 binary64) y)) < -1e5 or 2 < (/.f64 (-.f64 x y) (-.f64 #s(literal 1 binary64) y))

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 98.0

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

   5. Simplified 98.0%

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

   if -1e5 < (/.f64 (-.f64 x y) (-.f64 #s(literal 1 binary64) y)) < 0.40000000000000002

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

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

      2. frac-2neg N/A

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

      3. associate-/r/ N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. neg-sub0 N/A

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

      7. associate--r- N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. +-lowering-+.f64 N/A

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

      11. neg-sub0 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate--r+ N/A

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

      15. neg-sub0 N/A

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

      16. remove-double-neg N/A

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

      17. --lowering--.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 98.0

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

   7. Simplified 98.0%

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

   if 0.40000000000000002 < (/.f64 (-.f64 x y) (-.f64 #s(literal 1 binary64) y)) < 2

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 97.5%

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

Alternative 4: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{1 - y}\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_0 \leq 10^{-24}:\\ \;\;\;\;0 - y\\ \mathbf{elif}\;t\_0 \leq 500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- 1.0 y))))
   (if (<= t_0 -5e-66)
     x
     (if (<= t_0 1e-24) (- 0.0 y) (if (<= t_0 500.0) 1.0 x)))))

C

double code(double x, double y) {
	double t_0 = (x - y) / (1.0 - y);
	double tmp;
	if (t_0 <= -5e-66) {
		tmp = x;
	} else if (t_0 <= 1e-24) {
		tmp = 0.0 - y;
	} else if (t_0 <= 500.0) {
		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) :: t_0
    real(8) :: tmp
    t_0 = (x - y) / (1.0d0 - y)
    if (t_0 <= (-5d-66)) then
        tmp = x
    else if (t_0 <= 1d-24) then
        tmp = 0.0d0 - y
    else if (t_0 <= 500.0d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) / (1.0 - y);
	double tmp;
	if (t_0 <= -5e-66) {
		tmp = x;
	} else if (t_0 <= 1e-24) {
		tmp = 0.0 - y;
	} else if (t_0 <= 500.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / (1.0 - y)
	tmp = 0
	if t_0 <= -5e-66:
		tmp = x
	elif t_0 <= 1e-24:
		tmp = 0.0 - y
	elif t_0 <= 500.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(1.0 - y))
	tmp = 0.0
	if (t_0 <= -5e-66)
		tmp = x;
	elseif (t_0 <= 1e-24)
		tmp = Float64(0.0 - y);
	elseif (t_0 <= 500.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / (1.0 - y);
	tmp = 0.0;
	if (t_0 <= -5e-66)
		tmp = x;
	elseif (t_0 <= 1e-24)
		tmp = 0.0 - y;
	elseif (t_0 <= 500.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e-66], x, If[LessEqual[t$95$0, 1e-24], N[(0.0 - y), $MachinePrecision], If[LessEqual[t$95$0, 500.0], 1.0, x]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 1 binary64) y)) < -4.99999999999999962e-66 or 500 < (/.f64 (-.f64 x y) (-.f64 #s(literal 1 binary64) y))

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 57.7%

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

   if -4.99999999999999962e-66 < (/.f64 (-.f64 x y) (-.f64 #s(literal 1 binary64) y)) < 9.99999999999999924e-25

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. +-lowering-+.f64 100.0

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

      2. neg-sub0 N/A

         \[\leadsto \color{blue}{0 - y} \]

      3. --lowering--.f64 66.2

         \[\leadsto \color{blue}{0 - y} \]

   8. Simplified 66.2%

      \[\leadsto \color{blue}{0 - y} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

      2. neg-lowering-neg.f64 66.2

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

   10. Applied egg-rr 66.2%

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

   if 9.99999999999999924e-25 < (/.f64 (-.f64 x y) (-.f64 #s(literal 1 binary64) y)) < 500

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 93.4%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{1 - y} \leq -5 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{x - y}{1 - y} \leq 10^{-24}:\\ \;\;\;\;0 - y\\ \mathbf{elif}\;\frac{x - y}{1 - y} \leq 500:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\left(-1 - y\right) \cdot \left(y - x\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{0 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   1.0
   (if (<= y 1.0)
     (* (- -1.0 y) (- y x))
     (if (<= y 4.9e+92) (/ x (- 0.0 y)) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = (-1.0 - y) * (y - x);
	} else if (y <= 4.9e+92) {
		tmp = x / (0.0 - y);
	} else {
		tmp = 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)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = ((-1.0d0) - y) * (y - x)
    else if (y <= 4.9d+92) then
        tmp = x / (0.0d0 - y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = (-1.0 - y) * (y - x);
	} else if (y <= 4.9e+92) {
		tmp = x / (0.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 1.0:
		tmp = (-1.0 - y) * (y - x)
	elif y <= 4.9e+92:
		tmp = x / (0.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = Float64(Float64(-1.0 - y) * Float64(y - x));
	elseif (y <= 4.9e+92)
		tmp = Float64(x / Float64(0.0 - y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = (-1.0 - y) * (y - x);
	elseif (y <= 4.9e+92)
		tmp = x / (0.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 1.0], N[(N[(-1.0 - y), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e+92], N[(x / N[(0.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 4.9000000000000002e92 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 79.8%

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

   if -1 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

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

      2. frac-2neg N/A

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

      3. associate-/r/ N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. neg-sub0 N/A

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

      7. associate--r- N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. +-lowering-+.f64 N/A

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

      11. neg-sub0 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate--r+ N/A

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

      15. neg-sub0 N/A

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

      16. remove-double-neg N/A

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

      17. --lowering--.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 98.2

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

   7. Simplified 98.2%

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

   if 1 < y < 4.9000000000000002e92

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 61.7

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

   5. Simplified 61.7%

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

      1. div-inv N/A

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

      2. *-commutative N/A

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

      3. flip3-- N/A

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

      4. clear-num N/A

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

      5. *-lowering-*.f64 N/A

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

      6. clear-num N/A

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

      7. flip3-- N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-neg-in N/A

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

      11. +-commutative N/A

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

      12. /-lowering-/.f64 N/A

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

      13. neg-sub0 N/A

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

      14. +-commutative N/A

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

      15. associate--r+ N/A

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

      16. metadata-eval N/A

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

      17. --lowering--.f64 61.5

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

   7. Applied egg-rr 61.5%

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

   8. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 57.5

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

   10. Simplified 57.5%

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

       1. associate-*l/ N/A

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

       2. associate-/l* N/A

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

       3. neg-mul-1 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x}{y}\right)} \]

       4. neg-lowering-neg.f64 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x}{y}\right)} \]

       5. /-lowering-/.f64 57.7

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

   12. Applied egg-rr 57.7%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\left(-1 - y\right) \cdot \left(y - x\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{0 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double t_0 = 1.0 + ((1.0 - x) / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 1.0) {
		tmp = (-1.0 - y) * (y - x);
	} 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 + ((1.0d0 - x) / y)
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 1.0d0) then
        tmp = ((-1.0d0) - y) * (y - x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. sub-neg N/A

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

      4. div-sub N/A

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

      5. +-lowering-+.f64 N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. /-lowering-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. --lowering--.f64 98.3

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

   5. Simplified 98.3%

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

   if -1 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

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

      2. frac-2neg N/A

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

      3. associate-/r/ N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. neg-sub0 N/A

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

      7. associate--r- N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. +-lowering-+.f64 N/A

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

      11. neg-sub0 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate--r+ N/A

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

      15. neg-sub0 N/A

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

      16. remove-double-neg N/A

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

      17. --lowering--.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 98.2

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

   7. Simplified 98.2%

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

Alternative 7: 86.2% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 71.3%

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

   if -1 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

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

      2. frac-2neg N/A

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

      3. associate-/r/ N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. neg-sub0 N/A

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

      7. associate--r- N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. +-lowering-+.f64 N/A

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

      11. neg-sub0 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate--r+ N/A

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

      15. neg-sub0 N/A

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

      16. remove-double-neg N/A

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

      17. --lowering--.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 98.2

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

   7. Simplified 98.2%

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

Alternative 8: 85.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 71.3%

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

   if -1 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. +-lowering-+.f64 97.7

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

   5. Simplified 97.7%

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

4. Final simplification 83.6%

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

Alternative 9: 85.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -50:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -50.0) 1.0 (if (<= y 1.0) (- x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -50.0) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x - y;
	} else {
		tmp = 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 <= (-50.0d0)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x - y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -50.0) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x - y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -50.0:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x - y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -50.0)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = Float64(x - y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -50.0)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x - y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -50.0], 1.0, If[LessEqual[y, 1.0], N[(x - y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -50 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 71.3%

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

   if -50 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. +-lowering-+.f64 97.7

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

   5. Simplified 97.7%

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

   6. Taylor expanded in x around 0

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

   8. Simplified 97.4%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. neg-mul-1 N/A

         \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \]

      4. unsub-neg N/A

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

      5. --lowering--.f64 97.4

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

   10. Applied egg-rr 97.4%

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

Alternative 10: 73.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.235:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -0.235) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.235) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 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 <= (-0.235d0)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -0.235) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.235:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.235)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.235)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.235], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -0.23499999999999999 or 1 < y

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 70.9%

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

   if -0.23499999999999999 < y < 1

   1. Initial program 100.0%

      \[\frac{x - y}{1 - y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 66.6%

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

Alternative 11: 37.9% accurate, 18.0× 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 100.0%

   \[\frac{x - y}{1 - y} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Simplified 39.8%

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

Reproduce

herbie shell --seed 2024195 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))