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

Percentage Accurate: 100.0% → 100.0%

Time: 6.5s

Alternatives: 8

Speedup: 1.0×

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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y + 0.5, z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma x (+ y 0.5) z))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. div-inv N/A

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

   2. *-commutative N/A

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

   3. distribute-lft-out N/A

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

   4. fma-define N/A

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

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

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

   6. +-commutative N/A

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

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

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

   8. metadata-eval 100.0%

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

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + 0.5, z\right)} \]
5. Add Preprocessing

Alternative 2: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z + x \cdot y\\ \mathbf{if}\;y \leq -1400000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.5:\\ \;\;\;\;z + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ z (* x y))))
   (if (<= y -1400000.0) 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 <= -1400000.0) {
		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 <= (-1400000.0d0)) 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 <= -1400000.0) {
		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 <= -1400000.0:
		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 <= -1400000.0)
		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 <= -1400000.0)
		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, -1400000.0], 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 < -1.4e6 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 99.4%

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

   5. Simplified 99.4%

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

   if -1.4e6 < 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 98.0%

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

   5. Simplified 98.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1400000:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;y \leq 0.5:\\ \;\;\;\;z + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+49}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+139}:\\ \;\;\;\;z + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.95e+49) (* x y) (if (<= y 2.65e+139) (+ z (* x 0.5)) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.95e+49) {
		tmp = x * y;
	} else if (y <= 2.65e+139) {
		tmp = z + (x * 0.5);
	} 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 <= (-1.95d+49)) then
        tmp = x * y
    else if (y <= 2.65d+139) then
        tmp = z + (x * 0.5d0)
    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 <= -1.95e+49) {
		tmp = x * y;
	} else if (y <= 2.65e+139) {
		tmp = z + (x * 0.5);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.95e+49:
		tmp = x * y
	elif y <= 2.65e+139:
		tmp = z + (x * 0.5)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.95e+49)
		tmp = Float64(x * y);
	elseif (y <= 2.65e+139)
		tmp = Float64(z + Float64(x * 0.5));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.95e+49)
		tmp = x * y;
	elseif (y <= 2.65e+139)
		tmp = z + (x * 0.5);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.95e+49], N[(x * y), $MachinePrecision], If[LessEqual[y, 2.65e+139], N[(z + N[(x * 0.5), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95e49 or 2.65000000000000025e139 < 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 71.9%

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

   5. Simplified 71.9%

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

   if -1.95e49 < y < 2.65000000000000025e139

   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 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+49}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+139}:\\ \;\;\;\;z + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -52000000000000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -52000000000000.0) z (if (<= z 1.75e+102) (* x (+ y 0.5)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -52000000000000.0) {
		tmp = z;
	} else if (z <= 1.75e+102) {
		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 <= (-52000000000000.0d0)) then
        tmp = z
    else if (z <= 1.75d+102) 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 <= -52000000000000.0) {
		tmp = z;
	} else if (z <= 1.75e+102) {
		tmp = x * (y + 0.5);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -52000000000000.0:
		tmp = z
	elif z <= 1.75e+102:
		tmp = x * (y + 0.5)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -52000000000000.0)
		tmp = z;
	elseif (z <= 1.75e+102)
		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 <= -52000000000000.0)
		tmp = z;
	elseif (z <= 1.75e+102)
		tmp = x * (y + 0.5);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -52000000000000.0], z, If[LessEqual[z, 1.75e+102], N[(x * N[(y + 0.5), $MachinePrecision]), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e13 or 1.75000000000000005e102 < 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 75.1%

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

   if -5.2e13 < z < 1.75000000000000005e102

   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 79.6%

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

   5. Simplified 79.6%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -52000000000000:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+48}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+136}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.2e+48) (* x y) (if (<= y 3.9e+136) z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.2e+48) {
		tmp = x * y;
	} else if (y <= 3.9e+136) {
		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 <= (-6.2d+48)) then
        tmp = x * y
    else if (y <= 3.9d+136) 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 <= -6.2e+48) {
		tmp = x * y;
	} else if (y <= 3.9e+136) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.2e+48:
		tmp = x * y
	elif y <= 3.9e+136:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.2e+48)
		tmp = Float64(x * y);
	elseif (y <= 3.9e+136)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.2e+48)
		tmp = x * y;
	elseif (y <= 3.9e+136)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.2e+48], N[(x * y), $MachinePrecision], If[LessEqual[y, 3.9e+136], z, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.20000000000000011e48 or 3.90000000000000019e136 < 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 71.5%

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

   5. Simplified 71.5%

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

   if -6.20000000000000011e48 < y < 3.90000000000000019e136

   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 56.8%

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

Alternative 6: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-114}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2e-114) z (if (<= z 2.1e-26) (* x 0.5) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e-114) {
		tmp = z;
	} else if (z <= 2.1e-26) {
		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 <= (-2d-114)) then
        tmp = z
    else if (z <= 2.1d-26) 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 <= -2e-114) {
		tmp = z;
	} else if (z <= 2.1e-26) {
		tmp = x * 0.5;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e-114:
		tmp = z
	elif z <= 2.1e-26:
		tmp = x * 0.5
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2e-114)
		tmp = z;
	elseif (z <= 2.1e-26)
		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 <= -2e-114)
		tmp = z;
	elseif (z <= 2.1e-26)
		tmp = x * 0.5;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2e-114], z, If[LessEqual[z, 2.1e-26], N[(x * 0.5), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e-114 or 2.10000000000000008e-26 < 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 64.0%

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

   if -2.0000000000000001e-114 < z < 2.10000000000000008e-26

   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 87.9%

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

   5. Simplified 87.9%

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

   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 43.4%

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

   8. Simplified 43.4%

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

Alternative 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / 2.0d0) + (x * y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 8: 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 46.6%

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

Reproduce

herbie shell --seed 2024161 
(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))