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

Percentage Accurate: 99.9% → 99.9%

Time: 7.5s

Alternatives: 8

Speedup: 1.0×

• 29.3% 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: 88.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot z\\ t_2 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-6}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 235000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* y z))) (t_2 (* y (+ z (* x y)))))
   (if (<= y -1.7e-13)
     t_2
     (if (<= y 2.35e-70)
       t_1
       (if (<= y 4.5e-6)
         (+ t (* x (* y y)))
         (if (<= y 235000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + (y * z);
	double t_2 = y * (z + (x * y));
	double tmp;
	if (y <= -1.7e-13) {
		tmp = t_2;
	} else if (y <= 2.35e-70) {
		tmp = t_1;
	} else if (y <= 4.5e-6) {
		tmp = t + (x * (y * y));
	} else if (y <= 235000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = t + (y * z)
    t_2 = y * (z + (x * y))
    if (y <= (-1.7d-13)) then
        tmp = t_2
    else if (y <= 2.35d-70) then
        tmp = t_1
    else if (y <= 4.5d-6) then
        tmp = t + (x * (y * y))
    else if (y <= 235000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t + (y * z);
	double t_2 = y * (z + (x * y));
	double tmp;
	if (y <= -1.7e-13) {
		tmp = t_2;
	} else if (y <= 2.35e-70) {
		tmp = t_1;
	} else if (y <= 4.5e-6) {
		tmp = t + (x * (y * y));
	} else if (y <= 235000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + (y * z)
	t_2 = y * (z + (x * y))
	tmp = 0
	if y <= -1.7e-13:
		tmp = t_2
	elif y <= 2.35e-70:
		tmp = t_1
	elif y <= 4.5e-6:
		tmp = t + (x * (y * y))
	elif y <= 235000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(y * z))
	t_2 = Float64(y * Float64(z + Float64(x * y)))
	tmp = 0.0
	if (y <= -1.7e-13)
		tmp = t_2;
	elseif (y <= 2.35e-70)
		tmp = t_1;
	elseif (y <= 4.5e-6)
		tmp = Float64(t + Float64(x * Float64(y * y)));
	elseif (y <= 235000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + (y * z);
	t_2 = y * (z + (x * y));
	tmp = 0.0;
	if (y <= -1.7e-13)
		tmp = t_2;
	elseif (y <= 2.35e-70)
		tmp = t_1;
	elseif (y <= 4.5e-6)
		tmp = t + (x * (y * y));
	elseif (y <= 235000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e-13], t$95$2, If[LessEqual[y, 2.35e-70], t$95$1, If[LessEqual[y, 4.5e-6], N[(t + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 235000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.70000000000000008e-13 or 2.35e8 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 94.9%

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

   if -1.70000000000000008e-13 < y < 2.3499999999999999e-70 or 4.50000000000000011e-6 < y < 2.35e8

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 91.2%

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

   if 2.3499999999999999e-70 < y < 4.50000000000000011e-6

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 87.4%

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

      1. unpow2 87.4%

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

   4. Simplified 87.4%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-70}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-6}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 235000000:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]

Alternative 3: 89.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-13} \lor \neg \left(y \leq 255000000\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9e-13) (not (<= y 255000000.0)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e-13) || !(y <= 255000000.0)) {
		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 <= (-9d-13)) .or. (.not. (y <= 255000000.0d0))) 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 <= -9e-13) || !(y <= 255000000.0)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9e-13) or not (y <= 255000000.0):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9e-13) || !(y <= 255000000.0))
		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 <= -9e-13) || ~((y <= 255000000.0)))
		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, -9e-13], N[Not[LessEqual[y, 255000000.0]], $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 < -9e-13 or 2.55e8 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 94.9%

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

   if -9e-13 < y < 2.55e8

   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 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-13} \lor \neg \left(y \leq 255000000\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 4: 88.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+49} \lor \neg \left(z \leq 2.3 \cdot 10^{+71}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.55e+49) (not (<= z 2.3e+71)))
   (+ t (* y z))
   (+ t (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.55e+49) || !(z <= 2.3e+71)) {
		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 <= (-1.55d+49)) .or. (.not. (z <= 2.3d+71))) 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 <= -1.55e+49) || !(z <= 2.3e+71)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.55e+49) or not (z <= 2.3e+71):
		tmp = t + (y * z)
	else:
		tmp = t + (y * (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.55e+49) || !(z <= 2.3e+71))
		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 <= -1.55e+49) || ~((z <= 2.3e+71)))
		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, -1.55e+49], N[Not[LessEqual[z, 2.3e+71]], $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 < -1.54999999999999996e49 or 2.3000000000000002e71 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 89.1%

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

   if -1.54999999999999996e49 < z < 2.3000000000000002e71

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 95.2%

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot y + t \]
   3. Step-by-step derivation

      1. *-commutative 95.2%

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

   4. Simplified 95.2%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+49} \lor \neg \left(z \leq 2.3 \cdot 10^{+71}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 5: 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 6: 51.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+156}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.5e+156) (* y z) (if (<= z 2.3e+119) t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+156) {
		tmp = y * z;
	} else if (z <= 2.3e+119) {
		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+156)) then
        tmp = y * z
    else if (z <= 2.3d+119) 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+156) {
		tmp = y * z;
	} else if (z <= 2.3e+119) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.5e+156:
		tmp = y * z
	elif z <= 2.3e+119:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.5e+156)
		tmp = Float64(y * z);
	elseif (z <= 2.3e+119)
		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+156)
		tmp = y * z;
	elseif (z <= 2.3e+119)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.5e+156], N[(y * z), $MachinePrecision], If[LessEqual[z, 2.3e+119], t, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e156 or 2.3000000000000001e119 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 86.9%

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

   3. Taylor expanded in y around 0 79.0%

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

   if -1.5e156 < z < 2.3000000000000001e119

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 47.5%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+156}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7: 66.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ t + y \cdot z \end{array} \]

FPCore

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

C

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

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)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 66.2%

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

3. Final simplification 66.2%

   \[\leadsto t + y \cdot z \]

Alternative 8: 38.6% 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 37.8%

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

3. Final simplification 37.8%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023277 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))