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

Percentage Accurate: 99.9% → 99.9%

Time: 9.0s

Alternatives: 9

Speedup: 1.0×

• 29.5% 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. Final simplification 99.9%

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

Alternative 2: 88.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-90}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+34}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))))
   (if (<= y -1.75e-40)
     t_1
     (if (<= y 1.1e-90)
       (+ t (* y z))
       (if (<= y 4e+34) (+ t (* x (* y y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -1.75e-40) {
		tmp = t_1;
	} else if (y <= 1.1e-90) {
		tmp = t + (y * z);
	} else if (y <= 4e+34) {
		tmp = t + (x * (y * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z + (x * y))
    if (y <= (-1.75d-40)) then
        tmp = t_1
    else if (y <= 1.1d-90) then
        tmp = t + (y * z)
    else if (y <= 4d+34) then
        tmp = t + (x * (y * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -1.75e-40) {
		tmp = t_1;
	} else if (y <= 1.1e-90) {
		tmp = t + (y * z);
	} else if (y <= 4e+34) {
		tmp = t + (x * (y * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z + (x * y))
	tmp = 0
	if y <= -1.75e-40:
		tmp = t_1
	elif y <= 1.1e-90:
		tmp = t + (y * z)
	elif y <= 4e+34:
		tmp = t + (x * (y * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z + Float64(x * y)))
	tmp = 0.0
	if (y <= -1.75e-40)
		tmp = t_1;
	elseif (y <= 1.1e-90)
		tmp = Float64(t + Float64(y * z));
	elseif (y <= 4e+34)
		tmp = Float64(t + Float64(x * Float64(y * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z + (x * y));
	tmp = 0.0;
	if (y <= -1.75e-40)
		tmp = t_1;
	elseif (y <= 1.1e-90)
		tmp = t + (y * z);
	elseif (y <= 4e+34)
		tmp = t + (x * (y * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e-40], t$95$1, If[LessEqual[y, 1.1e-90], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+34], N[(t + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7500000000000001e-40 or 3.99999999999999978e34 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 92.1%

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

   if -1.7500000000000001e-40 < y < 1.09999999999999993e-90

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 95.9%

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

   if 1.09999999999999993e-90 < y < 3.99999999999999978e34

   1. Initial program 99.7%

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

      1. add-cube-cbrt 98.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}} + t \]

      2. pow3 98.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right)}^{3}} + t \]

      3. *-commutative 98.7%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{y \cdot \left(x \cdot y + z\right)}}\right)}^{3} + t \]

      4. fma-def 98.7%

         \[\leadsto {\left(\sqrt[3]{y \cdot \color{blue}{\mathsf{fma}\left(x, y, z\right)}}\right)}^{3} + t \]

   3. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{y \cdot \mathsf{fma}\left(x, y, z\right)}\right)}^{3}} + t \]

   4. Taylor expanded in z around 0 81.8%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot x\right)} + t \]
   5. Step-by-step derivation

      1. pow-base-1 81.8%

         \[\leadsto \color{blue}{1} \cdot \left({y}^{2} \cdot x\right) + t \]

      2. *-lft-identity 81.8%

         \[\leadsto \color{blue}{{y}^{2} \cdot x} + t \]

      3. *-commutative 81.8%

         \[\leadsto \color{blue}{x \cdot {y}^{2}} + t \]

      4. unpow2 81.8%

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

   6. Simplified 81.8%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-90}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+34}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]

Alternative 3: 88.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+36}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))))
   (if (<= y -5e-41)
     t_1
     (if (<= y 3.8e-77)
       (+ t (* y z))
       (if (<= y 8.6e+36) (+ t (* y (* x y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -5e-41) {
		tmp = t_1;
	} else if (y <= 3.8e-77) {
		tmp = t + (y * z);
	} else if (y <= 8.6e+36) {
		tmp = t + (y * (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z + (x * y))
    if (y <= (-5d-41)) then
        tmp = t_1
    else if (y <= 3.8d-77) then
        tmp = t + (y * z)
    else if (y <= 8.6d+36) then
        tmp = t + (y * (x * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -5e-41) {
		tmp = t_1;
	} else if (y <= 3.8e-77) {
		tmp = t + (y * z);
	} else if (y <= 8.6e+36) {
		tmp = t + (y * (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z + (x * y))
	tmp = 0
	if y <= -5e-41:
		tmp = t_1
	elif y <= 3.8e-77:
		tmp = t + (y * z)
	elif y <= 8.6e+36:
		tmp = t + (y * (x * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z + Float64(x * y)))
	tmp = 0.0
	if (y <= -5e-41)
		tmp = t_1;
	elseif (y <= 3.8e-77)
		tmp = Float64(t + Float64(y * z));
	elseif (y <= 8.6e+36)
		tmp = Float64(t + Float64(y * Float64(x * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z + (x * y));
	tmp = 0.0;
	if (y <= -5e-41)
		tmp = t_1;
	elseif (y <= 3.8e-77)
		tmp = t + (y * z);
	elseif (y <= 8.6e+36)
		tmp = t + (y * (x * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e-41], t$95$1, If[LessEqual[y, 3.8e-77], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e+36], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999996e-41 or 8.6000000000000001e36 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 92.1%

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

   if -4.9999999999999996e-41 < y < 3.7999999999999999e-77

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 95.1%

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

   if 3.7999999999999999e-77 < y < 8.6000000000000001e36

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 83.7%

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

      1. unpow2 83.7%

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

      2. associate-*r* 83.8%

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

   4. Simplified 83.8%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+36}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]

Alternative 4: 88.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-42} \lor \neg \left(y \leq 5.6 \cdot 10^{-62}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.4e-42) (not (<= y 5.6e-62)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.4e-42) || !(y <= 5.6e-62)) {
		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 <= (-2.4d-42)) .or. (.not. (y <= 5.6d-62))) 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 <= -2.4e-42) || !(y <= 5.6e-62)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.4e-42) or not (y <= 5.6e-62):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.4e-42) || !(y <= 5.6e-62))
		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 <= -2.4e-42) || ~((y <= 5.6e-62)))
		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, -2.4e-42], N[Not[LessEqual[y, 5.6e-62]], $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 < -2.40000000000000003e-42 or 5.60000000000000005e-62 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 87.7%

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

   if -2.40000000000000003e-42 < y < 5.60000000000000005e-62

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 95.2%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-42} \lor \neg \left(y \leq 5.6 \cdot 10^{-62}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 5: 64.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-40} \lor \neg \left(y \leq 4.2 \cdot 10^{-62}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.3e-40) (not (<= y 4.2e-62))) (* y (* x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e-40) || !(y <= 4.2e-62)) {
		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 <= (-1.3d-40)) .or. (.not. (y <= 4.2d-62))) 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 <= -1.3e-40) || !(y <= 4.2e-62)) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.3e-40) or not (y <= 4.2e-62):
		tmp = y * (x * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.3e-40) || !(y <= 4.2e-62))
		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 <= -1.3e-40) || ~((y <= 4.2e-62)))
		tmp = y * (x * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.3e-40], N[Not[LessEqual[y, 4.2e-62]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -1.3000000000000001e-40 or 4.1999999999999998e-62 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 87.7%

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

   3. Taylor expanded in y around inf 63.1%

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

      1. unpow2 63.1%

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

      2. associate-*r* 65.0%

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

   5. Simplified 65.0%

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

   if -1.3000000000000001e-40 < y < 4.1999999999999998e-62

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 68.3%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-40} \lor \neg \left(y \leq 4.2 \cdot 10^{-62}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-40} \lor \neg \left(y \leq 1.25 \cdot 10^{+114}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.8e-40) (not (<= y 1.25e+114))) (* y (* x y)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e-40) || !(y <= 1.25e+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 <= (-1.8d-40)) .or. (.not. (y <= 1.25d+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 <= -1.8e-40) || !(y <= 1.25e+114)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.8e-40) or not (y <= 1.25e+114):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.8e-40) || !(y <= 1.25e+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 <= -1.8e-40) || ~((y <= 1.25e+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, -1.8e-40], N[Not[LessEqual[y, 1.25e+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 < -1.8e-40 or 1.25e114 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 93.7%

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

   3. Taylor expanded in y around inf 68.8%

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

      1. unpow2 68.8%

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

      2. associate-*r* 71.4%

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

   5. Simplified 71.4%

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

   if -1.8e-40 < y < 1.25e114

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 85.9%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-40} \lor \neg \left(y \leq 1.25 \cdot 10^{+114}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t + (y * (z + (x * y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 8: 51.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+23}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e+23) (* y z) (if (<= z 2.2e+81) t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+23) {
		tmp = y * z;
	} else if (z <= 2.2e+81) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.05d+23)) then
        tmp = y * z
    else if (z <= 2.2d+81) then
        tmp = t
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+23) {
		tmp = y * z;
	} else if (z <= 2.2e+81) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e+23:
		tmp = y * z
	elif z <= 2.2e+81:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e+23)
		tmp = Float64(y * z);
	elseif (z <= 2.2e+81)
		tmp = t;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.05e+23)
		tmp = y * z;
	elseif (z <= 2.2e+81)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e+23], N[(y * z), $MachinePrecision], If[LessEqual[z, 2.2e+81], t, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0500000000000001e23 or 2.19999999999999987e81 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 76.5%

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

   3. Taylor expanded in y around 0 62.1%

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

   if -1.0500000000000001e23 < z < 2.19999999999999987e81

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 48.1%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+23}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 9: 38.5% 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 37.6%

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

3. Final simplification 37.6%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))