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

Percentage Accurate: 99.9% → 99.9%

Time: 5.8s

Alternatives: 8

Speedup: 1.0×

• 29.2% 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: 78.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+118} \lor \neg \left(y \leq -2.2 \cdot 10^{+14} \lor \neg \left(y \leq -6.5 \cdot 10^{-5}\right) \land \left(y \leq 3.2 \cdot 10^{+84} \lor \neg \left(y \leq 1.02 \cdot 10^{+133}\right) \land y \leq 6.5 \cdot 10^{+183}\right)\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.1e+118)
         (not
          (or (<= y -2.2e+14)
              (and (not (<= y -6.5e-5))
                   (or (<= y 3.2e+84)
                       (and (not (<= y 1.02e+133)) (<= y 6.5e+183)))))))
   (* y (* x y))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e+118) || !((y <= -2.2e+14) || (!(y <= -6.5e-5) && ((y <= 3.2e+84) || (!(y <= 1.02e+133) && (y <= 6.5e+183)))))) {
		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 <= (-2.1d+118)) .or. (.not. (y <= (-2.2d+14)) .or. (.not. (y <= (-6.5d-5))) .and. (y <= 3.2d+84) .or. (.not. (y <= 1.02d+133)) .and. (y <= 6.5d+183))) 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 <= -2.1e+118) || !((y <= -2.2e+14) || (!(y <= -6.5e-5) && ((y <= 3.2e+84) || (!(y <= 1.02e+133) && (y <= 6.5e+183)))))) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.1e+118) or not ((y <= -2.2e+14) or (not (y <= -6.5e-5) and ((y <= 3.2e+84) or (not (y <= 1.02e+133) and (y <= 6.5e+183))))):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.1e+118) || !((y <= -2.2e+14) || (!(y <= -6.5e-5) && ((y <= 3.2e+84) || (!(y <= 1.02e+133) && (y <= 6.5e+183))))))
		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 <= -2.1e+118) || ~(((y <= -2.2e+14) || (~((y <= -6.5e-5)) && ((y <= 3.2e+84) || (~((y <= 1.02e+133)) && (y <= 6.5e+183)))))))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.1e+118], N[Not[Or[LessEqual[y, -2.2e+14], And[N[Not[LessEqual[y, -6.5e-5]], $MachinePrecision], Or[LessEqual[y, 3.2e+84], And[N[Not[LessEqual[y, 1.02e+133]], $MachinePrecision], LessEqual[y, 6.5e+183]]]]]], $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 < -2.1e118 or -2.2e14 < y < -6.49999999999999943e-5 or 3.2000000000000001e84 < y < 1.02e133 or 6.49999999999999983e183 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 96.8%

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

   3. Taylor expanded in y around inf 91.3%

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

   if -2.1e118 < y < -2.2e14 or -6.49999999999999943e-5 < y < 3.2000000000000001e84 or 1.02e133 < y < 6.49999999999999983e183

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 84.6%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+118} \lor \neg \left(y \leq -2.2 \cdot 10^{+14} \lor \neg \left(y \leq -6.5 \cdot 10^{-5}\right) \land \left(y \leq 3.2 \cdot 10^{+84} \lor \neg \left(y \leq 1.02 \cdot 10^{+133}\right) \land y \leq 6.5 \cdot 10^{+183}\right)\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 3: 48.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+147}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+77}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-53}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+73}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+168}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.5e+147)
   (* y z)
   (if (<= z -2.5e+122)
     t
     (if (<= z -5.5e+77)
       (* y z)
       (if (<= z 1.25e-53)
         t
         (if (<= z 6.5e+73) (* y z) (if (<= z 1.5e+168) t (* y z))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+147) {
		tmp = y * z;
	} else if (z <= -2.5e+122) {
		tmp = t;
	} else if (z <= -5.5e+77) {
		tmp = y * z;
	} else if (z <= 1.25e-53) {
		tmp = t;
	} else if (z <= 6.5e+73) {
		tmp = y * z;
	} else if (z <= 1.5e+168) {
		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 <= (-1.5d+147)) then
        tmp = y * z
    else if (z <= (-2.5d+122)) then
        tmp = t
    else if (z <= (-5.5d+77)) then
        tmp = y * z
    else if (z <= 1.25d-53) then
        tmp = t
    else if (z <= 6.5d+73) then
        tmp = y * z
    else if (z <= 1.5d+168) 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 <= -1.5e+147) {
		tmp = y * z;
	} else if (z <= -2.5e+122) {
		tmp = t;
	} else if (z <= -5.5e+77) {
		tmp = y * z;
	} else if (z <= 1.25e-53) {
		tmp = t;
	} else if (z <= 6.5e+73) {
		tmp = y * z;
	} else if (z <= 1.5e+168) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.5e+147:
		tmp = y * z
	elif z <= -2.5e+122:
		tmp = t
	elif z <= -5.5e+77:
		tmp = y * z
	elif z <= 1.25e-53:
		tmp = t
	elif z <= 6.5e+73:
		tmp = y * z
	elif z <= 1.5e+168:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.5e+147)
		tmp = Float64(y * z);
	elseif (z <= -2.5e+122)
		tmp = t;
	elseif (z <= -5.5e+77)
		tmp = Float64(y * z);
	elseif (z <= 1.25e-53)
		tmp = t;
	elseif (z <= 6.5e+73)
		tmp = Float64(y * z);
	elseif (z <= 1.5e+168)
		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 <= -1.5e+147)
		tmp = y * z;
	elseif (z <= -2.5e+122)
		tmp = t;
	elseif (z <= -5.5e+77)
		tmp = y * z;
	elseif (z <= 1.25e-53)
		tmp = t;
	elseif (z <= 6.5e+73)
		tmp = y * z;
	elseif (z <= 1.5e+168)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.5e+147], N[(y * z), $MachinePrecision], If[LessEqual[z, -2.5e+122], t, If[LessEqual[z, -5.5e+77], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.25e-53], t, If[LessEqual[z, 6.5e+73], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.5e+168], t, N[(y * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999997e147 or -2.49999999999999994e122 < z < -5.50000000000000036e77 or 1.25e-53 < z < 6.5000000000000001e73 or 1.4999999999999999e168 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 80.5%

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

   3. Taylor expanded in y around 0 64.6%

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

   if -1.49999999999999997e147 < z < -2.49999999999999994e122 or -5.50000000000000036e77 < z < 1.25e-53 or 6.5000000000000001e73 < z < 1.4999999999999999e168

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 53.4%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+147}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+77}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-53}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+73}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+168}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 65.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-111}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.76 \cdot 10^{-143}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 0.000215:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -2.55e-5)
     t_1
     (if (<= y -8e-111)
       t
       (if (<= y -1.76e-143) (* y z) (if (<= y 0.000215) t t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -2.55e-5) {
		tmp = t_1;
	} else if (y <= -8e-111) {
		tmp = t;
	} else if (y <= -1.76e-143) {
		tmp = y * z;
	} else if (y <= 0.000215) {
		tmp = t;
	} 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 * (x * y)
    if (y <= (-2.55d-5)) then
        tmp = t_1
    else if (y <= (-8d-111)) then
        tmp = t
    else if (y <= (-1.76d-143)) then
        tmp = y * z
    else if (y <= 0.000215d0) then
        tmp = t
    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 * (x * y);
	double tmp;
	if (y <= -2.55e-5) {
		tmp = t_1;
	} else if (y <= -8e-111) {
		tmp = t;
	} else if (y <= -1.76e-143) {
		tmp = y * z;
	} else if (y <= 0.000215) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	tmp = 0
	if y <= -2.55e-5:
		tmp = t_1
	elif y <= -8e-111:
		tmp = t
	elif y <= -1.76e-143:
		tmp = y * z
	elif y <= 0.000215:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * y))
	tmp = 0.0
	if (y <= -2.55e-5)
		tmp = t_1;
	elseif (y <= -8e-111)
		tmp = t;
	elseif (y <= -1.76e-143)
		tmp = Float64(y * z);
	elseif (y <= 0.000215)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x * y);
	tmp = 0.0;
	if (y <= -2.55e-5)
		tmp = t_1;
	elseif (y <= -8e-111)
		tmp = t;
	elseif (y <= -1.76e-143)
		tmp = y * z;
	elseif (y <= 0.000215)
		tmp = t;
	else
		tmp = t_1;
	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, -2.55e-5], t$95$1, If[LessEqual[y, -8e-111], t, If[LessEqual[y, -1.76e-143], N[(y * z), $MachinePrecision], If[LessEqual[y, 0.000215], t, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.54999999999999998e-5 or 2.14999999999999995e-4 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 87.3%

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

   3. Taylor expanded in y around inf 67.0%

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

   if -2.54999999999999998e-5 < y < -8.00000000000000071e-111 or -1.76000000000000005e-143 < y < 2.14999999999999995e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 73.0%

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

   if -8.00000000000000071e-111 < y < -1.76000000000000005e-143

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 85.9%

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

   3. Taylor expanded in y around 0 86.2%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-111}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.76 \cdot 10^{-143}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 0.000215:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 5: 88.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-138}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+55}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))))
   (if (<= y -4.8e-5)
     t_1
     (if (<= y 1.45e-138)
       (+ t (* y z))
       (if (<= y 4.1e+55) (+ t (* x (* y y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -4.8e-5) {
		tmp = t_1;
	} else if (y <= 1.45e-138) {
		tmp = t + (y * z);
	} else if (y <= 4.1e+55) {
		tmp = t + (x * (y * y));
	} 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 <= (-4.8d-5)) then
        tmp = t_1
    else if (y <= 1.45d-138) then
        tmp = t + (y * z)
    else if (y <= 4.1d+55) then
        tmp = t + (x * (y * y))
    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 <= -4.8e-5) {
		tmp = t_1;
	} else if (y <= 1.45e-138) {
		tmp = t + (y * z);
	} else if (y <= 4.1e+55) {
		tmp = t + (x * (y * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z + (x * y))
	tmp = 0
	if y <= -4.8e-5:
		tmp = t_1
	elif y <= 1.45e-138:
		tmp = t + (y * z)
	elif y <= 4.1e+55:
		tmp = t + (x * (y * y))
	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 <= -4.8e-5)
		tmp = t_1;
	elseif (y <= 1.45e-138)
		tmp = Float64(t + Float64(y * z));
	elseif (y <= 4.1e+55)
		tmp = Float64(t + Float64(x * Float64(y * y)));
	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 <= -4.8e-5)
		tmp = t_1;
	elseif (y <= 1.45e-138)
		tmp = t + (y * z);
	elseif (y <= 4.1e+55)
		tmp = t + (x * (y * y));
	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, -4.8e-5], t$95$1, If[LessEqual[y, 1.45e-138], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+55], N[(t + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8000000000000001e-5 or 4.09999999999999981e55 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 91.1%

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

   if -4.8000000000000001e-5 < y < 1.44999999999999987e-138

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 98.0%

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

   if 1.44999999999999987e-138 < y < 4.09999999999999981e55

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.1%

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

      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 81.2%

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

      1. unpow2 81.2%

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

      2. *-commutative 81.2%

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

   6. Simplified 81.2%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-138}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+55}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]

Alternative 6: 89.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00016 \lor \neg \left(y \leq 2.2 \cdot 10^{+52}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.00016) (not (<= y 2.2e+52)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.00016) || !(y <= 2.2e+52)) {
		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 <= (-0.00016d0)) .or. (.not. (y <= 2.2d+52))) 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 <= -0.00016) || !(y <= 2.2e+52)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -0.00016) or not (y <= 2.2e+52):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.00016) || !(y <= 2.2e+52))
		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 <= -0.00016) || ~((y <= 2.2e+52)))
		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, -0.00016], N[Not[LessEqual[y, 2.2e+52]], $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 < -1.60000000000000013e-4 or 2.2e52 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 91.1%

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

   if -1.60000000000000013e-4 < y < 2.2e52

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 89.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00016 \lor \neg \left(y \leq 2.2 \cdot 10^{+52}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 7: 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 8: 39.1% 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 41.9%

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

3. Final simplification 41.9%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023257 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))