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

Percentage Accurate: 99.9% → 99.9%

Time: 5.5s

Alternatives: 7

Speedup: 1.0×

• 29.0% 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, 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 2: 78.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \lor \neg \left(y \leq -1.4 \cdot 10^{-42} \lor \neg \left(y \leq -1.18 \cdot 10^{-54}\right) \land y \leq 2.6 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.8)
         (not
          (or (<= y -1.4e-42) (and (not (<= y -1.18e-54)) (<= y 2.6e-12)))))
   (* y (* x y))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.8) || !((y <= -1.4e-42) || (!(y <= -1.18e-54) && (y <= 2.6e-12)))) {
		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 <= (-5.8d0)) .or. (.not. (y <= (-1.4d-42)) .or. (.not. (y <= (-1.18d-54))) .and. (y <= 2.6d-12))) 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 <= -5.8) || !((y <= -1.4e-42) || (!(y <= -1.18e-54) && (y <= 2.6e-12)))) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.8) or not ((y <= -1.4e-42) or (not (y <= -1.18e-54) and (y <= 2.6e-12))):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.8) || !((y <= -1.4e-42) || (!(y <= -1.18e-54) && (y <= 2.6e-12))))
		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 <= -5.8) || ~(((y <= -1.4e-42) || (~((y <= -1.18e-54)) && (y <= 2.6e-12)))))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.8], N[Not[Or[LessEqual[y, -1.4e-42], And[N[Not[LessEqual[y, -1.18e-54]], $MachinePrecision], LessEqual[y, 2.6e-12]]]], $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 < -5.79999999999999982 or -1.39999999999999999e-42 < y < -1.17999999999999996e-54 or 2.59999999999999983e-12 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 94.7%

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

   3. Taylor expanded in y around inf 69.2%

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

   if -5.79999999999999982 < y < -1.39999999999999999e-42 or -1.17999999999999996e-54 < y < 2.59999999999999983e-12

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 89.9%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \lor \neg \left(y \leq -1.4 \cdot 10^{-42} \lor \neg \left(y \leq -1.18 \cdot 10^{-54}\right) \land y \leq 2.6 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 3: 89.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-85}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-7}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))))
   (if (<= y -1.95e+54)
     t_1
     (if (<= y -1.35e-85)
       (+ t (* x (* y y)))
       (if (<= y 1.45e-7) (+ 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 <= -1.95e+54) {
		tmp = t_1;
	} else if (y <= -1.35e-85) {
		tmp = t + (x * (y * y));
	} else if (y <= 1.45e-7) {
		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 <= (-1.95d+54)) then
        tmp = t_1
    else if (y <= (-1.35d-85)) then
        tmp = t + (x * (y * y))
    else if (y <= 1.45d-7) 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 <= -1.95e+54) {
		tmp = t_1;
	} else if (y <= -1.35e-85) {
		tmp = t + (x * (y * y));
	} else if (y <= 1.45e-7) {
		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 <= -1.95e+54:
		tmp = t_1
	elif y <= -1.35e-85:
		tmp = t + (x * (y * y))
	elif y <= 1.45e-7:
		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 <= -1.95e+54)
		tmp = t_1;
	elseif (y <= -1.35e-85)
		tmp = Float64(t + Float64(x * Float64(y * y)));
	elseif (y <= 1.45e-7)
		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 <= -1.95e+54)
		tmp = t_1;
	elseif (y <= -1.35e-85)
		tmp = t + (x * (y * y));
	elseif (y <= 1.45e-7)
		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, -1.95e+54], t$95$1, If[LessEqual[y, -1.35e-85], N[(t + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-7], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9500000000000001e54 or 1.4499999999999999e-7 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 96.7%

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

   if -1.9500000000000001e54 < y < -1.3500000000000001e-85

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. distribute-rgt-in 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in x around inf 84.3%

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

      1. unpow2 84.3%

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

      2. *-commutative 84.3%

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

   6. Simplified 84.3%

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

   if -1.3500000000000001e-85 < y < 1.4499999999999999e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 92.1%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-85}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-7}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]

Alternative 4: 88.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-85} \lor \neg \left(y \leq 1.05 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.35e-85) (not (<= y 1.05e-9)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.35e-85) || !(y <= 1.05e-9)) {
		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 <= (-1.35d-85)) .or. (.not. (y <= 1.05d-9))) 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 <= -1.35e-85) || !(y <= 1.05e-9)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.35e-85) or not (y <= 1.05e-9):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.35e-85) || !(y <= 1.05e-9))
		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 <= -1.35e-85) || ~((y <= 1.05e-9)))
		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, -1.35e-85], N[Not[LessEqual[y, 1.05e-9]], $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 < -1.3500000000000001e-85 or 1.0500000000000001e-9 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 91.2%

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

   if -1.3500000000000001e-85 < y < 1.0500000000000001e-9

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 92.1%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-85} \lor \neg \left(y \leq 1.05 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 5: 66.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-55} \lor \neg \left(y \leq 1.05 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.5e-55) (not (<= y 1.05e-8))) (* y (* x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e-55) || !(y <= 1.05e-8)) {
		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 <= (-7.5d-55)) .or. (.not. (y <= 1.05d-8))) 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 <= -7.5e-55) || !(y <= 1.05e-8)) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.5e-55) or not (y <= 1.05e-8):
		tmp = y * (x * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.5e-55) || !(y <= 1.05e-8))
		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 <= -7.5e-55) || ~((y <= 1.05e-8)))
		tmp = y * (x * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.5e-55], N[Not[LessEqual[y, 1.05e-8]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -7.50000000000000023e-55 or 1.04999999999999997e-8 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 92.2%

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

   3. Taylor expanded in y around inf 66.7%

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

   if -7.50000000000000023e-55 < y < 1.04999999999999997e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 64.2%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-55} \lor \neg \left(y \leq 1.05 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 51.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+97}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-6}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.75e+97) (* y z) (if (<= z 6.4e-6) t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.75e+97) {
		tmp = y * z;
	} else if (z <= 6.4e-6) {
		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 <= (-1.75d+97)) then
        tmp = y * z
    else if (z <= 6.4d-6) 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 <= -1.75e+97) {
		tmp = y * z;
	} else if (z <= 6.4e-6) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.75e+97:
		tmp = y * z
	elif z <= 6.4e-6:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.75e+97)
		tmp = Float64(y * z);
	elseif (z <= 6.4e-6)
		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 <= -1.75e+97)
		tmp = y * z;
	elseif (z <= 6.4e-6)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.75e+97], N[(y * z), $MachinePrecision], If[LessEqual[z, 6.4e-6], t, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e97 or 6.3999999999999997e-6 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 80.9%

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

   3. Taylor expanded in y around 0 57.3%

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

   if -1.75e97 < z < 6.3999999999999997e-6

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 48.0%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+97}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-6}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7: 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 35.3%

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

3. Final simplification 35.3%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))