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

Percentage Accurate: 99.9% → 99.9%

Time: 5.0s

Alternatives: 7

Speedup: 1.0×

• 28.8% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot z\\ t_2 := y \cdot \left(x \cdot y + z\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+44}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* y z))) (t_2 (* y (+ (* x y) z))))
   (if (<= y -2.6e-22)
     t_2
     (if (<= y 2.55e-36)
       t_1
       (if (<= y 1.28e+44)
         (+ t (* y (* x y)))
         (if (<= y 1.65e+49) 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 * ((x * y) + z);
	double tmp;
	if (y <= -2.6e-22) {
		tmp = t_2;
	} else if (y <= 2.55e-36) {
		tmp = t_1;
	} else if (y <= 1.28e+44) {
		tmp = t + (y * (x * y));
	} else if (y <= 1.65e+49) {
		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 * ((x * y) + z)
    if (y <= (-2.6d-22)) then
        tmp = t_2
    else if (y <= 2.55d-36) then
        tmp = t_1
    else if (y <= 1.28d+44) then
        tmp = t + (y * (x * y))
    else if (y <= 1.65d+49) 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 * ((x * y) + z);
	double tmp;
	if (y <= -2.6e-22) {
		tmp = t_2;
	} else if (y <= 2.55e-36) {
		tmp = t_1;
	} else if (y <= 1.28e+44) {
		tmp = t + (y * (x * y));
	} else if (y <= 1.65e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + (y * z)
	t_2 = y * ((x * y) + z)
	tmp = 0
	if y <= -2.6e-22:
		tmp = t_2
	elif y <= 2.55e-36:
		tmp = t_1
	elif y <= 1.28e+44:
		tmp = t + (y * (x * y))
	elif y <= 1.65e+49:
		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(Float64(x * y) + z))
	tmp = 0.0
	if (y <= -2.6e-22)
		tmp = t_2;
	elseif (y <= 2.55e-36)
		tmp = t_1;
	elseif (y <= 1.28e+44)
		tmp = Float64(t + Float64(y * Float64(x * y)));
	elseif (y <= 1.65e+49)
		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 * ((x * y) + z);
	tmp = 0.0;
	if (y <= -2.6e-22)
		tmp = t_2;
	elseif (y <= 2.55e-36)
		tmp = t_1;
	elseif (y <= 1.28e+44)
		tmp = t + (y * (x * y));
	elseif (y <= 1.65e+49)
		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[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e-22], t$95$2, If[LessEqual[y, 2.55e-36], t$95$1, If[LessEqual[y, 1.28e+44], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+49], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e-22 or 1.6499999999999999e49 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 93.4%

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

   if -2.6e-22 < y < 2.54999999999999987e-36 or 1.28000000000000006e44 < y < 1.6499999999999999e49

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 96.8%

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

   if 2.54999999999999987e-36 < y < 1.28000000000000006e44

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 78.6%

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

      1. *-commutative 78.6%

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

   4. Simplified 78.6%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-36}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+44}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+49}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \end{array} \]

Alternative 3: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+199}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -4.4e-15)
     t_1
     (if (<= y 1.9e+45) t (if (<= y 1.45e+199) (* y z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -4.4e-15) {
		tmp = t_1;
	} else if (y <= 1.9e+45) {
		tmp = t;
	} else if (y <= 1.45e+199) {
		tmp = 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 * (x * y)
    if (y <= (-4.4d-15)) then
        tmp = t_1
    else if (y <= 1.9d+45) then
        tmp = t
    else if (y <= 1.45d+199) then
        tmp = 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 * (x * y);
	double tmp;
	if (y <= -4.4e-15) {
		tmp = t_1;
	} else if (y <= 1.9e+45) {
		tmp = t;
	} else if (y <= 1.45e+199) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	tmp = 0
	if y <= -4.4e-15:
		tmp = t_1
	elif y <= 1.9e+45:
		tmp = t
	elif y <= 1.45e+199:
		tmp = y * z
	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 <= -4.4e-15)
		tmp = t_1;
	elseif (y <= 1.9e+45)
		tmp = t;
	elseif (y <= 1.45e+199)
		tmp = Float64(y * z);
	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 <= -4.4e-15)
		tmp = t_1;
	elseif (y <= 1.9e+45)
		tmp = t;
	elseif (y <= 1.45e+199)
		tmp = y * z;
	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, -4.4e-15], t$95$1, If[LessEqual[y, 1.9e+45], t, If[LessEqual[y, 1.45e+199], N[(y * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.39999999999999971e-15 or 1.4499999999999999e199 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 93.9%

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

   3. Taylor expanded in z around 0 72.0%

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

   if -4.39999999999999971e-15 < y < 1.9000000000000001e45

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 67.2%

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

   if 1.9000000000000001e45 < y < 1.4499999999999999e199

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 92.0%

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

   3. Taylor expanded in z around inf 59.5%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+199}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 4: 89.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-23} \lor \neg \left(y \leq 1.8 \cdot 10^{+49}\right):\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.2e-23) (not (<= y 1.8e+49)))
   (* y (+ (* x y) z))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.2e-23) || !(y <= 1.8e+49)) {
		tmp = y * ((x * y) + z);
	} 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 <= (-6.2d-23)) .or. (.not. (y <= 1.8d+49))) then
        tmp = y * ((x * y) + z)
    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 <= -6.2e-23) || !(y <= 1.8e+49)) {
		tmp = y * ((x * y) + z);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.2e-23) or not (y <= 1.8e+49):
		tmp = y * ((x * y) + z)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.2e-23) || !(y <= 1.8e+49))
		tmp = Float64(y * Float64(Float64(x * y) + z));
	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 <= -6.2e-23) || ~((y <= 1.8e+49)))
		tmp = y * ((x * y) + z);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.2e-23], N[Not[LessEqual[y, 1.8e+49]], $MachinePrecision]], N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.1999999999999998e-23 or 1.79999999999999998e49 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 93.4%

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

   if -6.1999999999999998e-23 < y < 1.79999999999999998e49

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 90.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-23} \lor \neg \left(y \leq 1.8 \cdot 10^{+49}\right):\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 5: 77.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+51} \lor \neg \left(y \leq 1.52 \cdot 10^{+199}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.4e+51) (not (<= y 1.52e+199))) (* y (* x y)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.4e+51) || !(y <= 1.52e+199)) {
		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 <= (-2.4d+51)) .or. (.not. (y <= 1.52d+199))) 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 <= -2.4e+51) || !(y <= 1.52e+199)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.4e+51) or not (y <= 1.52e+199):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.4e+51) || !(y <= 1.52e+199))
		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 <= -2.4e+51) || ~((y <= 1.52e+199)))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.4e+51], N[Not[LessEqual[y, 1.52e+199]], $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 < -2.3999999999999999e51 or 1.51999999999999995e199 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 97.6%

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

   3. Taylor expanded in z around 0 77.5%

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

   if -2.3999999999999999e51 < y < 1.51999999999999995e199

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 83.1%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+51} \lor \neg \left(y \leq 1.52 \cdot 10^{+199}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 6: 48.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-53} \lor \neg \left(y \leq 1.35 \cdot 10^{+46}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.8e-53) (not (<= y 1.35e+46))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e-53) || !(y <= 1.35e+46)) {
		tmp = y * z;
	} 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 <= (-1.8d-53)) .or. (.not. (y <= 1.35d+46))) then
        tmp = y * z
    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 <= -1.8e-53) || !(y <= 1.35e+46)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.8e-53) or not (y <= 1.35e+46):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.8e-53) || !(y <= 1.35e+46))
		tmp = Float64(y * z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.8e-53) || ~((y <= 1.35e+46)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.8e-53], N[Not[LessEqual[y, 1.35e+46]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -1.7999999999999999e-53 or 1.3500000000000001e46 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 92.4%

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

   3. Taylor expanded in z around inf 41.5%

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

   if -1.7999999999999999e-53 < y < 1.3500000000000001e46

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 69.7%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-53} \lor \neg \left(y \leq 1.35 \cdot 10^{+46}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 38.8% 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 38.6%

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

3. Final simplification 38.6%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))