Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23

Percentage Accurate: 99.9% → 99.9%

Time: 5.6s

Alternatives: 8

Speedup: 1.0×

• 29.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot y + z\right) \cdot y + t \]
2. Step-by-step derivation

   1. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot y + z, y, t\right)} \]

   2. fma-def 100.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, y, z\right)}, y, t\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)} \]

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right) \]

Alternative 2: 64.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-93}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-24}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.028 \lor \neg \left(y \leq 1.16 \cdot 10^{+45}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -1.4e+80)
     t_1
     (if (<= y -1.4e-93)
       (* y z)
       (if (<= y 6.5e-24)
         t
         (if (or (<= y 0.028) (not (<= y 1.16e+45))) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -1.4e+80) {
		tmp = t_1;
	} else if (y <= -1.4e-93) {
		tmp = y * z;
	} else if (y <= 6.5e-24) {
		tmp = t;
	} else if ((y <= 0.028) || !(y <= 1.16e+45)) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * y)
    if (y <= (-1.4d+80)) then
        tmp = t_1
    else if (y <= (-1.4d-93)) then
        tmp = y * z
    else if (y <= 6.5d-24) then
        tmp = t
    else if ((y <= 0.028d0) .or. (.not. (y <= 1.16d+45))) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -1.4e+80) {
		tmp = t_1;
	} else if (y <= -1.4e-93) {
		tmp = y * z;
	} else if (y <= 6.5e-24) {
		tmp = t;
	} else if ((y <= 0.028) || !(y <= 1.16e+45)) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	tmp = 0
	if y <= -1.4e+80:
		tmp = t_1
	elif y <= -1.4e-93:
		tmp = y * z
	elif y <= 6.5e-24:
		tmp = t
	elif (y <= 0.028) or not (y <= 1.16e+45):
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * y))
	tmp = 0.0
	if (y <= -1.4e+80)
		tmp = t_1;
	elseif (y <= -1.4e-93)
		tmp = Float64(y * z);
	elseif (y <= 6.5e-24)
		tmp = t;
	elseif ((y <= 0.028) || !(y <= 1.16e+45))
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x * y);
	tmp = 0.0;
	if (y <= -1.4e+80)
		tmp = t_1;
	elseif (y <= -1.4e-93)
		tmp = y * z;
	elseif (y <= 6.5e-24)
		tmp = t;
	elseif ((y <= 0.028) || ~((y <= 1.16e+45)))
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+80], t$95$1, If[LessEqual[y, -1.4e-93], N[(y * z), $MachinePrecision], If[LessEqual[y, 6.5e-24], t, If[Or[LessEqual[y, 0.028], N[Not[LessEqual[y, 1.16e+45]], $MachinePrecision]], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.39999999999999992e80 or 6.5e-24 < y < 0.0280000000000000006 or 1.1600000000000001e45 < y

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around inf 76.3%

      \[\leadsto \color{blue}{{y}^{2} \cdot x} + t \]

   3. Taylor expanded in y around inf 73.8%

      \[\leadsto \color{blue}{{y}^{2} \cdot x} \]
   4. Step-by-step derivation

      1. unpow2 73.8%

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

      2. associate-*r* 71.5%

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

   5. Simplified 71.5%

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

   if -1.39999999999999992e80 < y < -1.39999999999999999e-93

   1. Initial program 99.8%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around 0 76.0%

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

   3. Taylor expanded in z around inf 48.4%

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

   if -1.39999999999999999e-93 < y < 6.5e-24 or 0.0280000000000000006 < y < 1.1600000000000001e45

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in y around 0 69.2%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-93}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-24}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.028 \lor \neg \left(y \leq 1.16 \cdot 10^{+45}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-52} \lor \neg \left(y \leq 1.15 \cdot 10^{-24} \lor \neg \left(y \leq 0.0225\right) \land y \leq 4 \cdot 10^{+44}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8e-52)
         (not (or (<= y 1.15e-24) (and (not (<= y 0.0225)) (<= y 4e+44)))))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e-52) || !((y <= 1.15e-24) || (!(y <= 0.0225) && (y <= 4e+44)))) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-8d-52)) .or. (.not. (y <= 1.15d-24) .or. (.not. (y <= 0.0225d0)) .and. (y <= 4d+44))) then
        tmp = y * (z + (x * y))
    else
        tmp = t + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e-52) || !((y <= 1.15e-24) || (!(y <= 0.0225) && (y <= 4e+44)))) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8e-52) or not ((y <= 1.15e-24) or (not (y <= 0.0225) and (y <= 4e+44))):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8e-52) || !((y <= 1.15e-24) || (!(y <= 0.0225) && (y <= 4e+44))))
		tmp = Float64(y * Float64(z + Float64(x * y)));
	else
		tmp = Float64(t + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8e-52) || ~(((y <= 1.15e-24) || (~((y <= 0.0225)) && (y <= 4e+44)))))
		tmp = y * (z + (x * y));
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8e-52], N[Not[Or[LessEqual[y, 1.15e-24], And[N[Not[LessEqual[y, 0.0225]], $MachinePrecision], LessEqual[y, 4e+44]]]], $MachinePrecision]], N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.0000000000000001e-52 or 1.1500000000000001e-24 < y < 0.022499999999999999 or 4.0000000000000004e44 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 91.5%

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

   if -8.0000000000000001e-52 < y < 1.1500000000000001e-24 or 0.022499999999999999 < y < 4.0000000000000004e44

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around 0 93.7%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-52} \lor \neg \left(y \leq 1.15 \cdot 10^{-24} \lor \neg \left(y \leq 0.0225\right) \land y \leq 4 \cdot 10^{+44}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 4: 78.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+121} \lor \neg \left(y \leq 8.5 \cdot 10^{-24} \lor \neg \left(y \leq 5.5 \cdot 10^{-5}\right) \land y \leq 3.4 \cdot 10^{+45}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.5e+121)
         (not (or (<= y 8.5e-24) (and (not (<= y 5.5e-5)) (<= y 3.4e+45)))))
   (* y (* x y))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e+121) || !((y <= 8.5e-24) || (!(y <= 5.5e-5) && (y <= 3.4e+45)))) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-7.5d+121)) .or. (.not. (y <= 8.5d-24) .or. (.not. (y <= 5.5d-5)) .and. (y <= 3.4d+45))) then
        tmp = y * (x * y)
    else
        tmp = t + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e+121) || !((y <= 8.5e-24) || (!(y <= 5.5e-5) && (y <= 3.4e+45)))) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.5e+121) or not ((y <= 8.5e-24) or (not (y <= 5.5e-5) and (y <= 3.4e+45))):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.5e+121) || !((y <= 8.5e-24) || (!(y <= 5.5e-5) && (y <= 3.4e+45))))
		tmp = Float64(y * Float64(x * y));
	else
		tmp = Float64(t + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.5e+121) || ~(((y <= 8.5e-24) || (~((y <= 5.5e-5)) && (y <= 3.4e+45)))))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.5e+121], N[Not[Or[LessEqual[y, 8.5e-24], And[N[Not[LessEqual[y, 5.5e-5]], $MachinePrecision], LessEqual[y, 3.4e+45]]]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.49999999999999965e121 or 8.5000000000000002e-24 < y < 5.5000000000000002e-5 or 3.4e45 < y

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around inf 77.6%

      \[\leadsto \color{blue}{{y}^{2} \cdot x} + t \]

   3. Taylor expanded in y around inf 76.7%

      \[\leadsto \color{blue}{{y}^{2} \cdot x} \]
   4. Step-by-step derivation

      1. unpow2 76.7%

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

      2. associate-*r* 74.1%

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

   5. Simplified 74.1%

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

   if -7.49999999999999965e121 < y < 8.5000000000000002e-24 or 5.5000000000000002e-5 < y < 3.4e45

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around 0 88.2%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+121} \lor \neg \left(y \leq 8.5 \cdot 10^{-24} \lor \neg \left(y \leq 5.5 \cdot 10^{-5}\right) \land y \leq 3.4 \cdot 10^{+45}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 5: 88.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+47} \lor \neg \left(z \leq 4.5 \cdot 10^{+114}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.4e+47) (not (<= z 4.5e+114)))
   (+ t (* y z))
   (+ t (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e+47) || !(z <= 4.5e+114)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.4d+47)) .or. (.not. (z <= 4.5d+114))) then
        tmp = t + (y * z)
    else
        tmp = t + (y * (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e+47) || !(z <= 4.5e+114)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.4e+47) or not (z <= 4.5e+114):
		tmp = t + (y * z)
	else:
		tmp = t + (y * (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.4e+47) || !(z <= 4.5e+114))
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(t + Float64(y * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.4e+47) || ~((z <= 4.5e+114)))
		tmp = t + (y * z);
	else
		tmp = t + (y * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.4e+47], N[Not[LessEqual[z, 4.5e+114]], $MachinePrecision]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.39999999999999994e47 or 4.5000000000000001e114 < z

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around 0 88.3%

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

   if -1.39999999999999994e47 < z < 4.5000000000000001e114

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around inf 91.9%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+47} \lor \neg \left(z \leq 4.5 \cdot 10^{+114}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot y + z\right) \cdot y + t \]

2. Final simplification 99.9%

   \[\leadsto t + y \cdot \left(z + x \cdot y\right) \]

Alternative 7: 51.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{+51}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+59}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.46e+51) (* y z) (if (<= z 3.8e+59) t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.46e+51) {
		tmp = y * z;
	} else if (z <= 3.8e+59) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.46d+51)) then
        tmp = y * z
    else if (z <= 3.8d+59) then
        tmp = t
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.46e+51) {
		tmp = y * z;
	} else if (z <= 3.8e+59) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.46e+51:
		tmp = y * z
	elif z <= 3.8e+59:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.46e+51)
		tmp = Float64(y * z);
	elseif (z <= 3.8e+59)
		tmp = t;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.46e+51)
		tmp = y * z;
	elseif (z <= 3.8e+59)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.46e+51], N[(y * z), $MachinePrecision], If[LessEqual[z, 3.8e+59], t, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4600000000000001e51 or 3.8000000000000001e59 < z

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around 0 84.8%

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

   3. Taylor expanded in z around inf 64.4%

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

   if -1.4600000000000001e51 < z < 3.8000000000000001e59

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in y around 0 46.8%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{+51}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+59}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 8: 38.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 99.9%

   \[\left(x \cdot y + z\right) \cdot y + t \]

2. Taylor expanded in y around 0 36.1%

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

3. Final simplification 36.1%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))