Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

Alternatives: 7

Speedup: 1.3×

Specification

Math

\[\begin{array}{l} \\ \left(\frac{x}{2} + y \cdot x\right) + z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ (/ x 2.0) (* y x)) z))

C

double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x / 2.0d0) + (y * x)) + z
end function

Java

public static double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}

Python

def code(x, y, z):
	return ((x / 2.0) + (y * x)) + z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x / 2.0) + Float64(y * x)) + z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x / 2.0) + (y * x)) + z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x / 2.0), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\frac{x}{2} + y \cdot x\right) + z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ (/ x 2.0) (* y x)) z))

C

double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x / 2.0d0) + (y * x)) + z
end function

Java

public static double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}

Python

def code(x, y, z):
	return ((x / 2.0) + (y * x)) + z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x / 2.0) + Float64(y * x)) + z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x / 2.0) + (y * x)) + z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x / 2.0), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ z + x \cdot \left(y - -0.5\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ z (* x (- y -0.5))))

C

double code(double x, double y, double z) {
	return z + (x * (y - -0.5));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z + (x * (y - (-0.5d0)))
end function

Java

public static double code(double x, double y, double z) {
	return z + (x * (y - -0.5));
}

Python

def code(x, y, z):
	return z + (x * (y - -0.5))

Julia

function code(x, y, z)
	return Float64(z + Float64(x * Float64(y - -0.5)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = z + (x * (y - -0.5));
end

Wolfram

code[x_, y_, z_] := N[(z + N[(x * N[(y - -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(\frac{x}{2} + y \cdot x\right) + z \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. distribute-lft-in N/A

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

   2. *-commutative N/A

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

   3. +-commutative N/A

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

   4. associate-+r+ N/A

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

   5. metadata-eval N/A

      \[\leadsto \left(z + x \cdot y\right) + \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right) \cdot x \]

   6. distribute-lft-neg-in N/A

      \[\leadsto \left(z + x \cdot y\right) + \left(\mathsf{neg}\left(\frac{-1}{2} \cdot x\right)\right) \]

   7. unsub-neg N/A

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

   8. associate-+r- N/A

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

   9. cancel-sign-sub-inv N/A

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

   10. metadata-eval N/A

       \[\leadsto z + \left(x \cdot y + \frac{1}{2} \cdot x\right) \]

   11. *-commutative N/A

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

   12. distribute-lft-in N/A

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

   13. remove-double-neg N/A

       \[\leadsto z + x \cdot \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \frac{1}{2}\right) \]

   14. mul-1-neg N/A

       \[\leadsto z + x \cdot \left(\left(\mathsf{neg}\left(-1 \cdot y\right)\right) + \frac{1}{2}\right) \]

   15. neg-sub0 N/A

       \[\leadsto z + x \cdot \left(\left(0 - -1 \cdot y\right) + \frac{1}{2}\right) \]

   16. associate--r- N/A

       \[\leadsto z + x \cdot \left(0 - \color{blue}{\left(-1 \cdot y - \frac{1}{2}\right)}\right) \]

   17. neg-sub0 N/A

       \[\leadsto z + x \cdot \left(\mathsf{neg}\left(\left(-1 \cdot y - \frac{1}{2}\right)\right)\right) \]

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

       \[\leadsto z + \left(\mathsf{neg}\left(x \cdot \left(-1 \cdot y - \frac{1}{2}\right)\right)\right) \]

   19. neg-sub0 N/A

       \[\leadsto z + \left(0 - \color{blue}{x \cdot \left(-1 \cdot y - \frac{1}{2}\right)}\right) \]

   20. associate-+r- N/A

       \[\leadsto \left(z + 0\right) - \color{blue}{x \cdot \left(-1 \cdot y - \frac{1}{2}\right)} \]

   21. +-rgt-identity N/A

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

   22. --lowering--.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(z, \color{blue}{\left(x \cdot \left(-1 \cdot y - \frac{1}{2}\right)\right)}\right) \]

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

       \[\leadsto \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot y - \frac{1}{2}\right)}\right)\right) \]

   24. sub-neg N/A

       \[\leadsto \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(x, \left(-1 \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}\right)\right)\right) \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{z - x \cdot \left(-0.5 - y\right)} \]

6. Final simplification 100.0%

   \[\leadsto z + x \cdot \left(y - -0.5\right) \]
7. Add Preprocessing

Alternative 2: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z + x \cdot y\\ \mathbf{if}\;y \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.5:\\ \;\;\;\;z + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ z (* x y))))
   (if (<= y -0.5) t_0 (if (<= y 0.5) (+ z (* x 0.5)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z + (x * y);
	double tmp;
	if (y <= -0.5) {
		tmp = t_0;
	} else if (y <= 0.5) {
		tmp = z + (x * 0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z + (x * y)
    if (y <= (-0.5d0)) then
        tmp = t_0
    else if (y <= 0.5d0) then
        tmp = z + (x * 0.5d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z + (x * y);
	double tmp;
	if (y <= -0.5) {
		tmp = t_0;
	} else if (y <= 0.5) {
		tmp = z + (x * 0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z + (x * y)
	tmp = 0
	if y <= -0.5:
		tmp = t_0
	elif y <= 0.5:
		tmp = z + (x * 0.5)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z + Float64(x * y))
	tmp = 0.0
	if (y <= -0.5)
		tmp = t_0;
	elseif (y <= 0.5)
		tmp = Float64(z + Float64(x * 0.5));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z + (x * y);
	tmp = 0.0;
	if (y <= -0.5)
		tmp = t_0;
	elseif (y <= 0.5)
		tmp = z + (x * 0.5);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.5], t$95$0, If[LessEqual[y, 0.5], N[(z + N[(x * 0.5), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.5 or 0.5 < y

   1. Initial program 100.0%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, z\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 98.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   5. Simplified 98.5%

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

   if -0.5 < y < 0.5

   1. Initial program 100.0%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot x\right)}, z\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \frac{1}{2}\right), z\right) \]

      2. *-lowering-*.f64 98.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), z\right) \]

   5. Simplified 98.2%

      \[\leadsto \color{blue}{x \cdot 0.5} + z \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.5:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;y \leq 0.5:\\ \;\;\;\;z + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + 0.5\right)\\ \mathbf{if}\;y \leq -0.116:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2050:\\ \;\;\;\;z + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y 0.5))))
   (if (<= y -0.116) t_0 (if (<= y 2050.0) (+ z (* x 0.5)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + 0.5);
	double tmp;
	if (y <= -0.116) {
		tmp = t_0;
	} else if (y <= 2050.0) {
		tmp = z + (x * 0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y + 0.5d0)
    if (y <= (-0.116d0)) then
        tmp = t_0
    else if (y <= 2050.0d0) then
        tmp = z + (x * 0.5d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y + 0.5);
	double tmp;
	if (y <= -0.116) {
		tmp = t_0;
	} else if (y <= 2050.0) {
		tmp = z + (x * 0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + 0.5)
	tmp = 0
	if y <= -0.116:
		tmp = t_0
	elif y <= 2050.0:
		tmp = z + (x * 0.5)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + 0.5))
	tmp = 0.0
	if (y <= -0.116)
		tmp = t_0;
	elseif (y <= 2050.0)
		tmp = Float64(z + Float64(x * 0.5));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y + 0.5);
	tmp = 0.0;
	if (y <= -0.116)
		tmp = t_0;
	elseif (y <= 2050.0)
		tmp = z + (x * 0.5);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.116], t$95$0, If[LessEqual[y, 2050.0], N[(z + N[(x * 0.5), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.116000000000000006 or 2050 < y

   1. Initial program 100.0%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + y\right)}\right) \]

      2. +-lowering-+.f64 77.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{y}\right)\right) \]

   5. Simplified 77.4%

      \[\leadsto \color{blue}{x \cdot \left(0.5 + y\right)} \]

   if -0.116000000000000006 < y < 2050

   1. Initial program 100.0%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\frac{1}{2} \cdot x\right)}, z\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \frac{1}{2}\right), z\right) \]

      2. *-lowering-*.f64 98.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), z\right) \]

   5. Simplified 98.2%

      \[\leadsto \color{blue}{x \cdot 0.5} + z \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.116:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;y \leq 2050:\\ \;\;\;\;z + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+57}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.2e+57) z (if (<= z 3.6e+50) (* x (+ y 0.5)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.2e+57) {
		tmp = z;
	} else if (z <= 3.6e+50) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.2d+57)) then
        tmp = z
    else if (z <= 3.6d+50) then
        tmp = x * (y + 0.5d0)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.2e+57) {
		tmp = z;
	} else if (z <= 3.6e+50) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.2e+57:
		tmp = z
	elif z <= 3.6e+50:
		tmp = x * (y + 0.5)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.2e+57)
		tmp = z;
	elseif (z <= 3.6e+50)
		tmp = Float64(x * Float64(y + 0.5));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.2e+57)
		tmp = z;
	elseif (z <= 3.6e+50)
		tmp = x * (y + 0.5);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.2e+57], z, If[LessEqual[z, 3.6e+50], N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000029e57 or 3.59999999999999986e50 < z

   1. Initial program 100.0%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 69.3%

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

   if -3.20000000000000029e57 < z < 3.59999999999999986e50

   1. Initial program 100.0%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + y\right)}\right) \]

      2. +-lowering-+.f64 82.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{y}\right)\right) \]

   5. Simplified 82.3%

      \[\leadsto \color{blue}{x \cdot \left(0.5 + y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+57}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1050:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+49}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1050.0) (* x y) (if (<= y 4.4e+49) z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1050.0) {
		tmp = x * y;
	} else if (y <= 4.4e+49) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1050.0d0)) then
        tmp = x * y
    else if (y <= 4.4d+49) then
        tmp = z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1050.0) {
		tmp = x * y;
	} else if (y <= 4.4e+49) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1050.0:
		tmp = x * y
	elif y <= 4.4e+49:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1050.0)
		tmp = Float64(x * y);
	elseif (y <= 4.4e+49)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1050.0)
		tmp = x * y;
	elseif (y <= 4.4e+49)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1050.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 4.4e+49], z, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1050 or 4.4000000000000001e49 < y

   1. Initial program 100.0%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 79.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 79.4%

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

   if -1050 < y < 4.4000000000000001e49

   1. Initial program 100.0%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 56.3%

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

Alternative 6: 51.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-52}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-54}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05e-52) z (if (<= z 4.5e-54) (* x 0.5) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e-52) {
		tmp = z;
	} else if (z <= 4.5e-54) {
		tmp = x * 0.5;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.05d-52)) then
        tmp = z
    else if (z <= 4.5d-54) then
        tmp = x * 0.5d0
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e-52) {
		tmp = z;
	} else if (z <= 4.5e-54) {
		tmp = x * 0.5;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.05e-52:
		tmp = z
	elif z <= 4.5e-54:
		tmp = x * 0.5
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05e-52)
		tmp = z;
	elseif (z <= 4.5e-54)
		tmp = Float64(x * 0.5);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.05e-52)
		tmp = z;
	elseif (z <= 4.5e-54)
		tmp = x * 0.5;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05e-52], z, If[LessEqual[z, 4.5e-54], N[(x * 0.5), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0499999999999999e-52 or 4.4999999999999998e-54 < z

   1. Initial program 100.0%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 60.7%

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

   if -1.0499999999999999e-52 < z < 4.4999999999999998e-54

   1. Initial program 100.0%

      \[\left(\frac{x}{2} + y \cdot x\right) + z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} + y\right)}\right) \]

      2. +-lowering-+.f64 91.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\frac{1}{2}, \color{blue}{y}\right)\right) \]

   5. Simplified 91.2%

      \[\leadsto \color{blue}{x \cdot \left(0.5 + y\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot x} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\frac{1}{2}} \]

      2. *-lowering-*.f64 37.6%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{2}}\right) \]

   8. Simplified 37.6%

      \[\leadsto \color{blue}{x \cdot 0.5} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 40.6% accurate, 9.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 z)

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return z

Julia

function code(x, y, z)
	return z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 100.0%

   \[\left(\frac{x}{2} + y \cdot x\right) + z \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Simplified 40.8%

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

Reproduce

herbie shell --seed 2024145 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2.0) (* y x)) z))