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

Percentage Accurate: 99.9% → 99.9%

Time: 7.3s

Alternatives: 8

Speedup: 1.0×

• 29.6% 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. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto t + y \cdot \left(x \cdot y + z\right) \]
4. Add Preprocessing

Alternative 2: 88.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y + z\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-81}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-6}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ (* x y) z))))
   (if (<= y -5.5e+84)
     t_1
     (if (<= y -2.4e-81)
       (+ t (* x (* y y)))
       (if (<= y 6.1e-6) (+ t (* y z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * ((x * y) + z);
	double tmp;
	if (y <= -5.5e+84) {
		tmp = t_1;
	} else if (y <= -2.4e-81) {
		tmp = t + (x * (y * y));
	} else if (y <= 6.1e-6) {
		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 * ((x * y) + z)
    if (y <= (-5.5d+84)) then
        tmp = t_1
    else if (y <= (-2.4d-81)) then
        tmp = t + (x * (y * y))
    else if (y <= 6.1d-6) 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 * ((x * y) + z);
	double tmp;
	if (y <= -5.5e+84) {
		tmp = t_1;
	} else if (y <= -2.4e-81) {
		tmp = t + (x * (y * y));
	} else if (y <= 6.1e-6) {
		tmp = t + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * ((x * y) + z)
	tmp = 0
	if y <= -5.5e+84:
		tmp = t_1
	elif y <= -2.4e-81:
		tmp = t + (x * (y * y))
	elif y <= 6.1e-6:
		tmp = t + (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(Float64(x * y) + z))
	tmp = 0.0
	if (y <= -5.5e+84)
		tmp = t_1;
	elseif (y <= -2.4e-81)
		tmp = Float64(t + Float64(x * Float64(y * y)));
	elseif (y <= 6.1e-6)
		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 * ((x * y) + z);
	tmp = 0.0;
	if (y <= -5.5e+84)
		tmp = t_1;
	elseif (y <= -2.4e-81)
		tmp = t + (x * (y * y));
	elseif (y <= 6.1e-6)
		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[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+84], t$95$1, If[LessEqual[y, -2.4e-81], N[(t + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.1e-6], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000004e84 or 6.10000000000000004e-6 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 91.8%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{y \cdot \left(z + x \cdot y\right)}{t}\right)} \]
   4. Step-by-step derivation

      1. associate-/l* 91.7%

         \[\leadsto t \cdot \left(1 + \color{blue}{y \cdot \frac{z + x \cdot y}{t}}\right) \]

      2. +-commutative 91.7%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{x \cdot y + z}}{t}\right) \]

      3. *-commutative 91.7%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{y \cdot x} + z}{t}\right) \]

      4. fma-undefine 91.7%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{\mathsf{fma}\left(y, x, z\right)}}{t}\right) \]

   5. Simplified 91.7%

      \[\leadsto \color{blue}{t \cdot \left(1 + y \cdot \frac{\mathsf{fma}\left(y, x, z\right)}{t}\right)} \]

   6. Taylor expanded in t around 0 91.3%

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

   if -5.5000000000000004e84 < y < -2.3999999999999999e-81

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 91.8%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y \cdot z}{x} + {y}^{2}\right)} + t \]
   4. Step-by-step derivation

      1. +-commutative 91.8%

         \[\leadsto x \cdot \color{blue}{\left({y}^{2} + \frac{y \cdot z}{x}\right)} + t \]

      2. unpow2 91.8%

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

      3. associate-/l* 89.1%

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

      4. distribute-lft-out 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in y around inf 84.6%

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

   if -2.3999999999999999e-81 < y < 6.10000000000000004e-6

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 90.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-81}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-6}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+150} \lor \neg \left(z \leq 2.55 \cdot 10^{+123}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8e+150) (not (<= z 2.55e+123)))
   (+ t (* y z))
   (+ t (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+150) || !(z <= 2.55e+123)) {
		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 <= (-8d+150)) .or. (.not. (z <= 2.55d+123))) 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 <= -8e+150) || !(z <= 2.55e+123)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8e+150) or not (z <= 2.55e+123):
		tmp = t + (y * z)
	else:
		tmp = t + (y * (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8e+150) || !(z <= 2.55e+123))
		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 <= -8e+150) || ~((z <= 2.55e+123)))
		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, -8e+150], N[Not[LessEqual[z, 2.55e+123]], $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 < -7.99999999999999985e150 or 2.54999999999999986e123 < z

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 89.2%

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

   if -7.99999999999999985e150 < z < 2.54999999999999986e123

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 93.0%

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

      1. *-commutative 93.0%

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

   5. Simplified 93.0%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+150} \lor \neg \left(z \leq 2.55 \cdot 10^{+123}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+27} \lor \neg \left(y \leq 2.45 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.5e+27) (not (<= y 2.45e-9)))
   (* y (+ (* x y) z))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5e+27) || !(y <= 2.45e-9)) {
		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 <= (-3.5d+27)) .or. (.not. (y <= 2.45d-9))) 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 <= -3.5e+27) || !(y <= 2.45e-9)) {
		tmp = y * ((x * y) + z);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.5e+27) or not (y <= 2.45e-9):
		tmp = y * ((x * y) + z)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.5e+27) || !(y <= 2.45e-9))
		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 <= -3.5e+27) || ~((y <= 2.45e-9)))
		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, -3.5e+27], N[Not[LessEqual[y, 2.45e-9]], $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 < -3.5000000000000002e27 or 2.45000000000000002e-9 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 91.4%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{y \cdot \left(z + x \cdot y\right)}{t}\right)} \]
   4. Step-by-step derivation

      1. associate-/l* 91.3%

         \[\leadsto t \cdot \left(1 + \color{blue}{y \cdot \frac{z + x \cdot y}{t}}\right) \]

      2. +-commutative 91.3%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{x \cdot y + z}}{t}\right) \]

      3. *-commutative 91.3%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{y \cdot x} + z}{t}\right) \]

      4. fma-undefine 91.3%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{\mathsf{fma}\left(y, x, z\right)}}{t}\right) \]

   5. Simplified 91.3%

      \[\leadsto \color{blue}{t \cdot \left(1 + y \cdot \frac{\mathsf{fma}\left(y, x, z\right)}{t}\right)} \]

   6. Taylor expanded in t around 0 90.1%

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

   if -3.5000000000000002e27 < y < 2.45000000000000002e-9

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 86.7%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+27} \lor \neg \left(y \leq 2.45 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+29} \lor \neg \left(y \leq 3.6 \cdot 10^{+114}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.7e+29) (not (<= y 3.6e+114))) (* y (* x y)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.7e+29) || !(y <= 3.6e+114)) {
		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 <= (-1.7d+29)) .or. (.not. (y <= 3.6d+114))) 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 <= -1.7e+29) || !(y <= 3.6e+114)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.7e+29) or not (y <= 3.6e+114):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.7e+29) || !(y <= 3.6e+114))
		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 <= -1.7e+29) || ~((y <= 3.6e+114)))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.7e+29], N[Not[LessEqual[y, 3.6e+114]], $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 < -1.69999999999999991e29 or 3.6000000000000001e114 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 97.0%

      \[\leadsto \color{blue}{\left(z \cdot \left(1 + \frac{x \cdot y}{z}\right)\right)} \cdot y + t \]

   4. Taylor expanded in t around 0 91.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(1 + \frac{x \cdot y}{z}\right)\right)} \]

   5. Taylor expanded in z around 0 80.0%

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

   if -1.69999999999999991e29 < y < 3.6000000000000001e114

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.4%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+29} \lor \neg \left(y \leq 3.6 \cdot 10^{+114}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+22} \lor \neg \left(y \leq 1.4 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.8e+22) (not (<= y 1.4e-8))) (* y (* x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e+22) || !(y <= 1.4e-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 <= (-1.8d+22)) .or. (.not. (y <= 1.4d-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 <= -1.8e+22) || !(y <= 1.4e-8)) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.8e+22) or not (y <= 1.4e-8):
		tmp = y * (x * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.8e+22) || !(y <= 1.4e-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 <= -1.8e+22) || ~((y <= 1.4e-8)))
		tmp = y * (x * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.8e+22], N[Not[LessEqual[y, 1.4e-8]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e22 or 1.4e-8 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 95.6%

      \[\leadsto \color{blue}{\left(z \cdot \left(1 + \frac{x \cdot y}{z}\right)\right)} \cdot y + t \]

   4. Taylor expanded in t around 0 86.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(1 + \frac{x \cdot y}{z}\right)\right)} \]

   5. Taylor expanded in z around 0 71.0%

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

   if -1.8e22 < y < 1.4e-8

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 69.6%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+22} \lor \neg \left(y \leq 1.4 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+48} \lor \neg \left(z \leq 1.4 \cdot 10^{+180}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.5e+48) (not (<= z 1.4e+180))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.5e+48) || !(z <= 1.4e+180)) {
		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 ((z <= (-9.5d+48)) .or. (.not. (z <= 1.4d+180))) 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 ((z <= -9.5e+48) || !(z <= 1.4e+180)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.5e+48) or not (z <= 1.4e+180):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.5e+48) || !(z <= 1.4e+180))
		tmp = Float64(y * z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.5e+48) || ~((z <= 1.4e+180)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.5e+48], N[Not[LessEqual[z, 1.4e+180]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999997e48 or 1.40000000000000006e180 < z

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 91.2%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{y \cdot \left(z + x \cdot y\right)}{t}\right)} \]
   4. Step-by-step derivation

      1. associate-/l* 85.4%

         \[\leadsto t \cdot \left(1 + \color{blue}{y \cdot \frac{z + x \cdot y}{t}}\right) \]

      2. +-commutative 85.4%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{x \cdot y + z}}{t}\right) \]

      3. *-commutative 85.4%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{y \cdot x} + z}{t}\right) \]

      4. fma-undefine 85.4%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{\mathsf{fma}\left(y, x, z\right)}}{t}\right) \]

   5. Simplified 85.4%

      \[\leadsto \color{blue}{t \cdot \left(1 + y \cdot \frac{\mathsf{fma}\left(y, x, z\right)}{t}\right)} \]

   6. Taylor expanded in z around inf 59.5%

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

   if -9.4999999999999997e48 < z < 1.40000000000000006e180

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 47.8%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+48} \lor \neg \left(z \leq 1.4 \cdot 10^{+180}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.8% 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. Add Preprocessing

3. Taylor expanded in y around 0 39.4%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024137 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))