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

Percentage Accurate: 99.9% → 99.9%

Time: 6.6s

Alternatives: 9

Speedup: 1.0×

• 29.4% 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 99.9%

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

   2. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 79.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+109} \lor \neg \left(y \leq -1.9 \cdot 10^{+26} \lor \neg \left(y \leq -12500000000000\right) \land y \leq 2.1 \cdot 10^{+52}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.6e+109)
         (not
          (or (<= y -1.9e+26)
              (and (not (<= y -12500000000000.0)) (<= y 2.1e+52)))))
   (* y (* x y))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e+109) || !((y <= -1.9e+26) || (!(y <= -12500000000000.0) && (y <= 2.1e+52)))) {
		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 <= (-2.6d+109)) .or. (.not. (y <= (-1.9d+26)) .or. (.not. (y <= (-12500000000000.0d0))) .and. (y <= 2.1d+52))) 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 <= -2.6e+109) || !((y <= -1.9e+26) || (!(y <= -12500000000000.0) && (y <= 2.1e+52)))) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.6e+109) or not ((y <= -1.9e+26) or (not (y <= -12500000000000.0) and (y <= 2.1e+52))):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.6e+109) || !((y <= -1.9e+26) || (!(y <= -12500000000000.0) && (y <= 2.1e+52))))
		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 <= -2.6e+109) || ~(((y <= -1.9e+26) || (~((y <= -12500000000000.0)) && (y <= 2.1e+52)))))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.6e+109], N[Not[Or[LessEqual[y, -1.9e+26], And[N[Not[LessEqual[y, -12500000000000.0]], $MachinePrecision], LessEqual[y, 2.1e+52]]]], $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 < -2.5999999999999998e109 or -1.9000000000000001e26 < y < -1.25e13 or 2.1e52 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 93.7%

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

   3. Taylor expanded in y around inf 79.3%

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

   if -2.5999999999999998e109 < y < -1.9000000000000001e26 or -1.25e13 < y < 2.1e52

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 87.5%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+109} \lor \neg \left(y \leq -1.9 \cdot 10^{+26} \lor \neg \left(y \leq -12500000000000\right) \land y \leq 2.1 \cdot 10^{+52}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 3: 88.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-26}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+48}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))))
   (if (<= y -2.25e+114)
     t_1
     (if (<= y -2.5e-26)
       (+ t (* x (* y y)))
       (if (<= y 1.15e+48) (+ t (* y z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -2.25e+114) {
		tmp = t_1;
	} else if (y <= -2.5e-26) {
		tmp = t + (x * (y * y));
	} else if (y <= 1.15e+48) {
		tmp = t + (y * z);
	} else {
		tmp = t_1;
	}
	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 * (z + (x * y))
    if (y <= (-2.25d+114)) then
        tmp = t_1
    else if (y <= (-2.5d-26)) then
        tmp = t + (x * (y * y))
    else if (y <= 1.15d+48) then
        tmp = t + (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -2.25e+114) {
		tmp = t_1;
	} else if (y <= -2.5e-26) {
		tmp = t + (x * (y * y));
	} else if (y <= 1.15e+48) {
		tmp = t + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z + (x * y))
	tmp = 0
	if y <= -2.25e+114:
		tmp = t_1
	elif y <= -2.5e-26:
		tmp = t + (x * (y * y))
	elif y <= 1.15e+48:
		tmp = t + (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z + Float64(x * y)))
	tmp = 0.0
	if (y <= -2.25e+114)
		tmp = t_1;
	elseif (y <= -2.5e-26)
		tmp = Float64(t + Float64(x * Float64(y * y)));
	elseif (y <= 1.15e+48)
		tmp = Float64(t + Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z + (x * y));
	tmp = 0.0;
	if (y <= -2.25e+114)
		tmp = t_1;
	elseif (y <= -2.5e-26)
		tmp = t + (x * (y * y));
	elseif (y <= 1.15e+48)
		tmp = t + (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.25e+114], t$95$1, If[LessEqual[y, -2.5e-26], N[(t + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+48], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.25e114 or 1.15e48 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 93.4%

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

   if -2.25e114 < y < -2.5000000000000001e-26

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.2%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \sqrt[3]{x \cdot y + z}\right)} \cdot y + t \]

      2. pow3 99.2%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot y + z}\right)}^{3}} \cdot y + t \]

      3. fma-def 99.2%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(x, y, z\right)}}\right)}^{3} \cdot y + t \]

   3. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z\right)}\right)}^{3}} \cdot y + t \]

   4. Taylor expanded in x around inf 86.9%

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

      1. *-commutative 86.9%

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

      2. unpow2 86.9%

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

   6. Simplified 86.9%

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

   if -2.5000000000000001e-26 < y < 1.15e48

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 91.3%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-26}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+48}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]

Alternative 4: 51.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+151}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+35}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+61}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+123}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.9e+151)
   (* y z)
   (if (<= z 2.95e+35)
     t
     (if (<= z 7e+61) (* y z) (if (<= z 1.75e+123) t (* y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.9e+151) {
		tmp = y * z;
	} else if (z <= 2.95e+35) {
		tmp = t;
	} else if (z <= 7e+61) {
		tmp = y * z;
	} else if (z <= 1.75e+123) {
		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 <= (-3.9d+151)) then
        tmp = y * z
    else if (z <= 2.95d+35) then
        tmp = t
    else if (z <= 7d+61) then
        tmp = y * z
    else if (z <= 1.75d+123) 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 <= -3.9e+151) {
		tmp = y * z;
	} else if (z <= 2.95e+35) {
		tmp = t;
	} else if (z <= 7e+61) {
		tmp = y * z;
	} else if (z <= 1.75e+123) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.9e+151:
		tmp = y * z
	elif z <= 2.95e+35:
		tmp = t
	elif z <= 7e+61:
		tmp = y * z
	elif z <= 1.75e+123:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.9e+151)
		tmp = Float64(y * z);
	elseif (z <= 2.95e+35)
		tmp = t;
	elseif (z <= 7e+61)
		tmp = Float64(y * z);
	elseif (z <= 1.75e+123)
		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 <= -3.9e+151)
		tmp = y * z;
	elseif (z <= 2.95e+35)
		tmp = t;
	elseif (z <= 7e+61)
		tmp = y * z;
	elseif (z <= 1.75e+123)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.9e+151], N[(y * z), $MachinePrecision], If[LessEqual[z, 2.95e+35], t, If[LessEqual[z, 7e+61], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.75e+123], t, N[(y * z), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.89999999999999976e151 or 2.94999999999999993e35 < z < 7.00000000000000036e61 or 1.75e123 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 87.4%

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

   3. Taylor expanded in y around 0 68.6%

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

   if -3.89999999999999976e151 < z < 2.94999999999999993e35 or 7.00000000000000036e61 < z < 1.75e123

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 49.2%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+151}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+35}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+61}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+123}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5: 88.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6500000000 \lor \neg \left(y \leq 1.3 \cdot 10^{+48}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6500000000.0) (not (<= y 1.3e+48)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6500000000.0) || !(y <= 1.3e+48)) {
		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 <= (-6500000000.0d0)) .or. (.not. (y <= 1.3d+48))) 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 <= -6500000000.0) || !(y <= 1.3e+48)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6500000000.0) or not (y <= 1.3e+48):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6500000000.0) || !(y <= 1.3e+48))
		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 <= -6500000000.0) || ~((y <= 1.3e+48)))
		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, -6500000000.0], N[Not[LessEqual[y, 1.3e+48]], $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 < -6.5e9 or 1.29999999999999998e48 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 89.0%

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

   if -6.5e9 < y < 1.29999999999999998e48

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 89.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6500000000 \lor \neg \left(y \leq 1.3 \cdot 10^{+48}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 6: 87.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+95}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+124}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e+95)
   (+ t (* y z))
   (if (<= z 1.85e+124) (+ t (* y (* x y))) (* y (+ z (* x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+95) {
		tmp = t + (y * z);
	} else if (z <= 1.85e+124) {
		tmp = t + (y * (x * y));
	} else {
		tmp = y * (z + (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 <= (-2.3d+95)) then
        tmp = t + (y * z)
    else if (z <= 1.85d+124) then
        tmp = t + (y * (x * y))
    else
        tmp = y * (z + (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 <= -2.3e+95) {
		tmp = t + (y * z);
	} else if (z <= 1.85e+124) {
		tmp = t + (y * (x * y));
	} else {
		tmp = y * (z + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.3e+95:
		tmp = t + (y * z)
	elif z <= 1.85e+124:
		tmp = t + (y * (x * y))
	else:
		tmp = y * (z + (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e+95)
		tmp = Float64(t + Float64(y * z));
	elseif (z <= 1.85e+124)
		tmp = Float64(t + Float64(y * Float64(x * y)));
	else
		tmp = Float64(y * Float64(z + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.3e+95)
		tmp = t + (y * z);
	elseif (z <= 1.85e+124)
		tmp = t + (y * (x * y));
	else
		tmp = y * (z + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e+95], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+124], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.29999999999999997e95

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 85.9%

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

   if -2.29999999999999997e95 < z < 1.85000000000000004e124

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 92.6%

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

   if 1.85000000000000004e124 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 85.6%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+95}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+124}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]

Alternative 7: 65.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -720 \lor \neg \left(y \leq 2.75 \cdot 10^{+48}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -720.0) (not (<= y 2.75e+48))) (* y (* x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -720.0) || !(y <= 2.75e+48)) {
		tmp = y * (x * y);
	} 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) :: tmp
    if ((y <= (-720.0d0)) .or. (.not. (y <= 2.75d+48))) then
        tmp = y * (x * y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -720.0) || !(y <= 2.75e+48)) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -720.0) or not (y <= 2.75e+48):
		tmp = y * (x * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -720.0) || !(y <= 2.75e+48))
		tmp = Float64(y * Float64(x * y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -720.0) || ~((y <= 2.75e+48)))
		tmp = y * (x * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -720.0], N[Not[LessEqual[y, 2.75e+48]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -720 or 2.7500000000000001e48 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 89.0%

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

   3. Taylor expanded in y around inf 73.5%

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

   if -720 < y < 2.7500000000000001e48

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 63.1%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -720 \lor \neg \left(y \leq 2.75 \cdot 10^{+48}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 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 9: 39.2% 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 38.7%

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

3. Final simplification 38.7%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023224 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))