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

Percentage Accurate: 99.9% → 99.9%

Time: 7.6s

Alternatives: 9

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, 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-define 99.9%

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

   2. fma-define 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. Add Preprocessing

Alternative 2: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(z + N[(x * y), $MachinePrecision]), $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-define 99.9%

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

   2. fma-define 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. Step-by-step derivation

   1. fma-define 99.9%

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

6. Applied egg-rr 99.9%

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

7. Final simplification 99.9%

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

Alternative 3: 65.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -6800:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 10^{+43}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -6800.0) t_1 (if (<= y 3e-14) t (if (<= y 1e+43) (* 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 <= -6800.0) {
		tmp = t_1;
	} else if (y <= 3e-14) {
		tmp = t;
	} else if (y <= 1e+43) {
		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 <= (-6800.0d0)) then
        tmp = t_1
    else if (y <= 3d-14) then
        tmp = t
    else if (y <= 1d+43) 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 <= -6800.0) {
		tmp = t_1;
	} else if (y <= 3e-14) {
		tmp = t;
	} else if (y <= 1e+43) {
		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 <= -6800.0:
		tmp = t_1
	elif y <= 3e-14:
		tmp = t
	elif y <= 1e+43:
		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 <= -6800.0)
		tmp = t_1;
	elseif (y <= 3e-14)
		tmp = t;
	elseif (y <= 1e+43)
		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 <= -6800.0)
		tmp = t_1;
	elseif (y <= 3e-14)
		tmp = t;
	elseif (y <= 1e+43)
		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, -6800.0], t$95$1, If[LessEqual[y, 3e-14], t, If[LessEqual[y, 1e+43], N[(y * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6800 or 1.00000000000000001e43 < y

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in t around 0 89.2%

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

   8. Taylor expanded in z around 0 71.7%

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

   if -6800 < y < 2.9999999999999998e-14

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 63.1%

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

   if 2.9999999999999998e-14 < y < 1.00000000000000001e43

   1. Initial program 99.9%

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

      1. fma-define 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around inf 65.2%

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

Alternative 4: 89.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+47} \lor \neg \left(z \leq 4.6 \cdot 10^{+83}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e+47) (not (<= z 4.6e+83)))
   (+ t (* y z))
   (+ t (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e+47) || !(z <= 4.6e+83)) {
		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 <= (-2.8d+47)) .or. (.not. (z <= 4.6d+83))) 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 <= -2.8e+47) || !(z <= 4.6e+83)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e+47) or not (z <= 4.6e+83):
		tmp = t + (y * z)
	else:
		tmp = t + (y * (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.8e+47) || !(z <= 4.6e+83))
		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 <= -2.8e+47) || ~((z <= 4.6e+83)))
		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, -2.8e+47], N[Not[LessEqual[z, 4.6e+83]], $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 < -2.79999999999999988e47 or 4.5999999999999999e83 < 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 85.9%

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

   if -2.79999999999999988e47 < z < 4.5999999999999999e83

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 93.8%

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

      1. *-commutative 93.8%

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

   5. Simplified 93.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+47} \lor \neg \left(z \leq 4.6 \cdot 10^{+83}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -25500 \lor \neg \left(y \leq 4.3 \cdot 10^{+24}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -25500.0) (not (<= y 4.3e+24)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -25500.0) || !(y <= 4.3e+24)) {
		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 <= (-25500.0d0)) .or. (.not. (y <= 4.3d+24))) 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 <= -25500.0) || !(y <= 4.3e+24)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -25500.0) or not (y <= 4.3e+24):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -25500.0) || !(y <= 4.3e+24))
		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 <= -25500.0) || ~((y <= 4.3e+24)))
		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, -25500.0], N[Not[LessEqual[y, 4.3e+24]], $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 < -25500 or 4.29999999999999987e24 < y

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in t around 0 89.7%

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

   if -25500 < y < 4.29999999999999987e24

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 86.8%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -25500 \lor \neg \left(y \leq 4.3 \cdot 10^{+24}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+65} \lor \neg \left(y \leq 1.8 \cdot 10^{+144}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4e+65) (not (<= y 1.8e+144))) (* y (* x y)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4e+65) || !(y <= 1.8e+144)) {
		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 <= (-4d+65)) .or. (.not. (y <= 1.8d+144))) 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 <= -4e+65) || !(y <= 1.8e+144)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4e+65) or not (y <= 1.8e+144):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4e+65) || !(y <= 1.8e+144))
		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 <= -4e+65) || ~((y <= 1.8e+144)))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4e+65], N[Not[LessEqual[y, 1.8e+144]], $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 < -4e65 or 1.7999999999999999e144 < y

   1. Initial program 99.9%

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

      1. fma-define 99.9%

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

      2. fma-define 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. Step-by-step derivation

      1. fma-define 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 97.8%

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

   8. Taylor expanded in z around 0 80.8%

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

   if -4e65 < y < 1.7999999999999999e144

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.4%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+65} \lor \neg \left(y \leq 1.8 \cdot 10^{+144}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+48} \lor \neg \left(z \leq 2.1 \cdot 10^{+90}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e+48) (not (<= z 2.1e+90))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+48) || !(z <= 2.1e+90)) {
		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 <= (-6.2d+48)) .or. (.not. (z <= 2.1d+90))) 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 <= -6.2e+48) || !(z <= 2.1e+90)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2e+48) or not (z <= 2.1e+90):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e+48) || !(z <= 2.1e+90))
		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 <= -6.2e+48) || ~((z <= 2.1e+90)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e+48], N[Not[LessEqual[z, 2.1e+90]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000011e48 or 2.09999999999999981e90 < z

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-define 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around inf 68.1%

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

   if -6.20000000000000011e48 < z < 2.09999999999999981e90

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 46.5%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+48} \lor \neg \left(z \leq 2.1 \cdot 10^{+90}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
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: 39.3% 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 35.9%

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))