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

Percentage Accurate: 99.9% → 99.9%

Time: 7.6s

Alternatives: 9

Speedup: 1.0×

• 29.9% 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. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right) \]
6. Add Preprocessing

Alternative 2: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 99.9%

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

   1. +-commutative 99.9%

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

   2. *-commutative 99.9%

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

   3. fma-udef 99.9%

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

5. Simplified 99.9%

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

6. Final simplification 99.9%

   \[\leadsto t + y \cdot \mathsf{fma}\left(y, x, z\right) \]
7. Add Preprocessing

Alternative 3: 52.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+83} \lor \neg \left(z \leq -9 \cdot 10^{+30} \lor \neg \left(z \leq -7.2 \cdot 10^{+18}\right) \land z \leq 9 \cdot 10^{+91}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.7e+83)
         (not (or (<= z -9e+30) (and (not (<= z -7.2e+18)) (<= z 9e+91)))))
   (* y z)
   t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.7e+83) || !((z <= -9e+30) || (!(z <= -7.2e+18) && (z <= 9e+91)))) {
		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 <= (-4.7d+83)) .or. (.not. (z <= (-9d+30)) .or. (.not. (z <= (-7.2d+18))) .and. (z <= 9d+91))) 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 <= -4.7e+83) || !((z <= -9e+30) || (!(z <= -7.2e+18) && (z <= 9e+91)))) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.7e+83) or not ((z <= -9e+30) or (not (z <= -7.2e+18) and (z <= 9e+91))):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.7e+83) || !((z <= -9e+30) || (!(z <= -7.2e+18) && (z <= 9e+91))))
		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 <= -4.7e+83) || ~(((z <= -9e+30) || (~((z <= -7.2e+18)) && (z <= 9e+91)))))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.7e+83], N[Not[Or[LessEqual[z, -9e+30], And[N[Not[LessEqual[z, -7.2e+18]], $MachinePrecision], LessEqual[z, 9e+91]]]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -4.6999999999999999e83 or -8.9999999999999999e30 < z < -7.2e18 or 9e91 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 81.1%

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

   4. Taylor expanded in z around inf 59.5%

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

   if -4.6999999999999999e83 < z < -8.9999999999999999e30 or -7.2e18 < z < 9e91

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 50.7%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+83} \lor \neg \left(z \leq -9 \cdot 10^{+30} \lor \neg \left(z \leq -7.2 \cdot 10^{+18}\right) \land z \leq 9 \cdot 10^{+91}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+44}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -3.2e-15)
     t_1
     (if (<= y 7e-28) t (if (<= y 2.3e+44) (* 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 <= -3.2e-15) {
		tmp = t_1;
	} else if (y <= 7e-28) {
		tmp = t;
	} else if (y <= 2.3e+44) {
		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 <= (-3.2d-15)) then
        tmp = t_1
    else if (y <= 7d-28) then
        tmp = t
    else if (y <= 2.3d+44) 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 <= -3.2e-15) {
		tmp = t_1;
	} else if (y <= 7e-28) {
		tmp = t;
	} else if (y <= 2.3e+44) {
		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 <= -3.2e-15:
		tmp = t_1
	elif y <= 7e-28:
		tmp = t
	elif y <= 2.3e+44:
		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 <= -3.2e-15)
		tmp = t_1;
	elseif (y <= 7e-28)
		tmp = t;
	elseif (y <= 2.3e+44)
		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 <= -3.2e-15)
		tmp = t_1;
	elseif (y <= 7e-28)
		tmp = t;
	elseif (y <= 2.3e+44)
		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, -3.2e-15], t$95$1, If[LessEqual[y, 7e-28], t, If[LessEqual[y, 2.3e+44], N[(y * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1999999999999999e-15 or 2.30000000000000004e44 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 89.2%

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

   4. Taylor expanded in z around 0 73.2%

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

      1. *-commutative 73.2%

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

   6. Simplified 73.2%

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

   if -3.1999999999999999e-15 < y < 6.9999999999999999e-28

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.6%

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

   if 6.9999999999999999e-28 < y < 2.30000000000000004e44

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 71.1%

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

   4. Taylor expanded in z around inf 63.1%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+44}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-14} \lor \neg \left(y \leq 4.9 \cdot 10^{+36}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.4e-14) (not (<= y 4.9e+36)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e-14) || !(y <= 4.9e+36)) {
		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 <= (-1.4d-14)) .or. (.not. (y <= 4.9d+36))) 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 <= -1.4e-14) || !(y <= 4.9e+36)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.4e-14) or not (y <= 4.9e+36):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.4e-14) || !(y <= 4.9e+36))
		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 <= -1.4e-14) || ~((y <= 4.9e+36)))
		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, -1.4e-14], N[Not[LessEqual[y, 4.9e+36]], $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 < -1.4e-14 or 4.89999999999999981e36 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 89.5%

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

   if -1.4e-14 < y < 4.89999999999999981e36

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 90.6%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-14} \lor \neg \left(y \leq 4.9 \cdot 10^{+36}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+14}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+35}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.36e+14)
   (+ t (* y (* x y)))
   (if (<= y 3.2e+35) (+ t (* y z)) (* y (+ z (* x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.36e+14) {
		tmp = t + (y * (x * y));
	} else if (y <= 3.2e+35) {
		tmp = t + (y * z);
	} else {
		tmp = y * (z + (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 (y <= (-1.36d+14)) then
        tmp = t + (y * (x * y))
    else if (y <= 3.2d+35) then
        tmp = t + (y * z)
    else
        tmp = y * (z + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.36e+14) {
		tmp = t + (y * (x * y));
	} else if (y <= 3.2e+35) {
		tmp = t + (y * z);
	} else {
		tmp = y * (z + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.36e+14:
		tmp = t + (y * (x * y))
	elif y <= 3.2e+35:
		tmp = t + (y * z)
	else:
		tmp = y * (z + (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.36e+14)
		tmp = Float64(t + Float64(y * Float64(x * y)));
	elseif (y <= 3.2e+35)
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(y * Float64(z + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.36e+14)
		tmp = t + (y * (x * y));
	elseif (y <= 3.2e+35)
		tmp = t + (y * z);
	else
		tmp = y * (z + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.36e+14], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+35], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.36e14

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 86.9%

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

      1. *-commutative 86.9%

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

   5. Simplified 86.9%

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

   if -1.36e14 < y < 3.19999999999999983e35

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 89.5%

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

   if 3.19999999999999983e35 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 93.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+14}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+35}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+94} \lor \neg \left(y \leq 5.5 \cdot 10^{+47}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.65e+94) (not (<= y 5.5e+47))) (* y (* x y)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.65e+94) || !(y <= 5.5e+47)) {
		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 <= (-1.65d+94)) .or. (.not. (y <= 5.5d+47))) 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 <= -1.65e+94) || !(y <= 5.5e+47)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.65e+94) or not (y <= 5.5e+47):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.65e+94) || !(y <= 5.5e+47))
		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 <= -1.65e+94) || ~((y <= 5.5e+47)))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.65e+94], N[Not[LessEqual[y, 5.5e+47]], $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 < -1.65e94 or 5.4999999999999998e47 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 92.3%

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

   4. Taylor expanded in z around 0 79.9%

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

      1. *-commutative 79.9%

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

   6. Simplified 79.9%

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

   if -1.65e94 < y < 5.4999999999999998e47

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 87.2%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+94} \lor \neg \left(y \leq 5.5 \cdot 10^{+47}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 9: 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 39.6%

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

4. Final simplification 39.6%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))