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

Percentage Accurate: 100.0% → 100.0%

Time: 10.9s

Alternatives: 8

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, 1.0× 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]

Derivation

1. Initial program 100.0%

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

Alternative 2: 60.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -46000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-7}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-162}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-211}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-218}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1050000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -46000000.0)
   (* x y)
   (if (<= y -1.12e-7)
     z
     (if (<= y -3.1e-162)
       (* x 0.5)
       (if (<= y -6.4e-211)
         z
         (if (<= y 7.6e-218) (* x 0.5) (if (<= y 1050000.0) z (* x y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -46000000.0) {
		tmp = x * y;
	} else if (y <= -1.12e-7) {
		tmp = z;
	} else if (y <= -3.1e-162) {
		tmp = x * 0.5;
	} else if (y <= -6.4e-211) {
		tmp = z;
	} else if (y <= 7.6e-218) {
		tmp = x * 0.5;
	} else if (y <= 1050000.0) {
		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 <= (-46000000.0d0)) then
        tmp = x * y
    else if (y <= (-1.12d-7)) then
        tmp = z
    else if (y <= (-3.1d-162)) then
        tmp = x * 0.5d0
    else if (y <= (-6.4d-211)) then
        tmp = z
    else if (y <= 7.6d-218) then
        tmp = x * 0.5d0
    else if (y <= 1050000.0d0) 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 <= -46000000.0) {
		tmp = x * y;
	} else if (y <= -1.12e-7) {
		tmp = z;
	} else if (y <= -3.1e-162) {
		tmp = x * 0.5;
	} else if (y <= -6.4e-211) {
		tmp = z;
	} else if (y <= 7.6e-218) {
		tmp = x * 0.5;
	} else if (y <= 1050000.0) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -46000000.0:
		tmp = x * y
	elif y <= -1.12e-7:
		tmp = z
	elif y <= -3.1e-162:
		tmp = x * 0.5
	elif y <= -6.4e-211:
		tmp = z
	elif y <= 7.6e-218:
		tmp = x * 0.5
	elif y <= 1050000.0:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -46000000.0)
		tmp = Float64(x * y);
	elseif (y <= -1.12e-7)
		tmp = z;
	elseif (y <= -3.1e-162)
		tmp = Float64(x * 0.5);
	elseif (y <= -6.4e-211)
		tmp = z;
	elseif (y <= 7.6e-218)
		tmp = Float64(x * 0.5);
	elseif (y <= 1050000.0)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -46000000.0)
		tmp = x * y;
	elseif (y <= -1.12e-7)
		tmp = z;
	elseif (y <= -3.1e-162)
		tmp = x * 0.5;
	elseif (y <= -6.4e-211)
		tmp = z;
	elseif (y <= 7.6e-218)
		tmp = x * 0.5;
	elseif (y <= 1050000.0)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -46000000.0], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.12e-7], z, If[LessEqual[y, -3.1e-162], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, -6.4e-211], z, If[LessEqual[y, 7.6e-218], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 1050000.0], z, N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.6e7 or 1.05e6 < 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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.6e7 < y < -1.12e-7 or -3.0999999999999999e-162 < y < -6.39999999999999971e-211 or 7.5999999999999997e-218 < y < 1.05e6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.12e-7 < y < -3.0999999999999999e-162 or -6.39999999999999971e-211 < y < 7.5999999999999997e-218

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot y + z\\ \mathbf{if}\;y \leq -4000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.5:\\ \;\;\;\;x \cdot 0.5 + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* x y) z)))
   (if (<= y -4000000.0) t_0 (if (<= y 0.5) (+ (* x 0.5) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * y) + z;
	double tmp;
	if (y <= -4000000.0) {
		tmp = t_0;
	} else if (y <= 0.5) {
		tmp = (x * 0.5) + z;
	} 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) + z
    if (y <= (-4000000.0d0)) then
        tmp = t_0
    else if (y <= 0.5d0) then
        tmp = (x * 0.5d0) + z
    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) + z;
	double tmp;
	if (y <= -4000000.0) {
		tmp = t_0;
	} else if (y <= 0.5) {
		tmp = (x * 0.5) + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * y) + z
	tmp = 0
	if y <= -4000000.0:
		tmp = t_0
	elif y <= 0.5:
		tmp = (x * 0.5) + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * y) + z)
	tmp = 0.0
	if (y <= -4000000.0)
		tmp = t_0;
	elseif (y <= 0.5)
		tmp = Float64(Float64(x * 0.5) + z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * y) + z;
	tmp = 0.0;
	if (y <= -4000000.0)
		tmp = t_0;
	elseif (y <= 0.5)
		tmp = (x * 0.5) + z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[y, -4000000.0], t$95$0, If[LessEqual[y, 0.5], N[(N[(x * 0.5), $MachinePrecision] + z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -40000000:\\ \;\;\;\;x \cdot \left(y - -0.5\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+28}:\\ \;\;\;\;x \cdot 0.5 + z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -40000000.0)
   (* x (- y -0.5))
   (if (<= y 6.2e+28) (+ (* x 0.5) z) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -40000000.0) {
		tmp = x * (y - -0.5);
	} else if (y <= 6.2e+28) {
		tmp = (x * 0.5) + 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 <= (-40000000.0d0)) then
        tmp = x * (y - (-0.5d0))
    else if (y <= 6.2d+28) then
        tmp = (x * 0.5d0) + 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 <= -40000000.0) {
		tmp = x * (y - -0.5);
	} else if (y <= 6.2e+28) {
		tmp = (x * 0.5) + z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -40000000.0:
		tmp = x * (y - -0.5)
	elif y <= 6.2e+28:
		tmp = (x * 0.5) + z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -40000000.0)
		tmp = Float64(x * Float64(y - -0.5));
	elseif (y <= 6.2e+28)
		tmp = Float64(Float64(x * 0.5) + z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -40000000.0)
		tmp = x * (y - -0.5);
	elseif (y <= 6.2e+28)
		tmp = (x * 0.5) + z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -40000000.0], N[(x * N[(y - -0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+28], N[(N[(x * 0.5), $MachinePrecision] + z), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4e7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4e7 < y < 6.2000000000000001e28

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 6.2000000000000001e28 < 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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y - -0.5\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{-52}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-126}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- y -0.5))))
   (if (<= x -1.9e-52) t_0 (if (<= x 2.05e-126) z t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y - -0.5);
	double tmp;
	if (x <= -1.9e-52) {
		tmp = t_0;
	} else if (x <= 2.05e-126) {
		tmp = z;
	} 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 (x <= (-1.9d-52)) then
        tmp = t_0
    else if (x <= 2.05d-126) then
        tmp = z
    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 (x <= -1.9e-52) {
		tmp = t_0;
	} else if (x <= 2.05e-126) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y - -0.5)
	tmp = 0
	if x <= -1.9e-52:
		tmp = t_0
	elif x <= 2.05e-126:
		tmp = z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y - -0.5))
	tmp = 0.0
	if (x <= -1.9e-52)
		tmp = t_0;
	elseif (x <= 2.05e-126)
		tmp = z;
	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 (x <= -1.9e-52)
		tmp = t_0;
	elseif (x <= 2.05e-126)
		tmp = z;
	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[x, -1.9e-52], t$95$0, If[LessEqual[x, 2.05e-126], z, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9000000000000002e-52 or 2.0499999999999999e-126 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.9000000000000002e-52 < x < 2.0499999999999999e-126

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 51.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-24}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-26}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.2e-24) z (if (<= z 3.8e-26) (* x 0.5) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.2e-24) {
		tmp = z;
	} else if (z <= 3.8e-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 <= (-4.2d-24)) then
        tmp = z
    else if (z <= 3.8d-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 <= -4.2e-24) {
		tmp = z;
	} else if (z <= 3.8e-26) {
		tmp = x * 0.5;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.2e-24:
		tmp = z
	elif z <= 3.8e-26:
		tmp = x * 0.5
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.2e-24)
		tmp = z;
	elseif (z <= 3.8e-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 <= -4.2e-24)
		tmp = z;
	elseif (z <= 3.8e-26)
		tmp = x * 0.5;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.2e-24], z, If[LessEqual[z, 3.8e-26], N[(x * 0.5), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1999999999999999e-24 or 3.80000000000000015e-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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -4.1999999999999999e-24 < z < 3.80000000000000015e-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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((y + 0.5) * 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 = ((y + 0.5d0) * x) + z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

4. Applied egg-rr 0

   \[\leadsto expr\]
5. Add Preprocessing

Alternative 8: 40.1% 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 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(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))