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

Percentage Accurate: 99.9% → 99.9%

Time: 4.2s

Alternatives: 8

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: 78.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ t_2 := t + y \cdot z\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+175}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))) (t_2 (+ t (* y z))))
   (if (<= y -1.02e+124)
     t_1
     (if (<= y 2.95e-5)
       t_2
       (if (<= y 5e+15) (* x (* y y)) (if (<= y 8e+175) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double t_2 = t + (y * z);
	double tmp;
	if (y <= -1.02e+124) {
		tmp = t_1;
	} else if (y <= 2.95e-5) {
		tmp = t_2;
	} else if (y <= 5e+15) {
		tmp = x * (y * y);
	} else if (y <= 8e+175) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y * (x * y)
    t_2 = t + (y * z)
    if (y <= (-1.02d+124)) then
        tmp = t_1
    else if (y <= 2.95d-5) then
        tmp = t_2
    else if (y <= 5d+15) then
        tmp = x * (y * y)
    else if (y <= 8d+175) then
        tmp = t_2
    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 t_2 = t + (y * z);
	double tmp;
	if (y <= -1.02e+124) {
		tmp = t_1;
	} else if (y <= 2.95e-5) {
		tmp = t_2;
	} else if (y <= 5e+15) {
		tmp = x * (y * y);
	} else if (y <= 8e+175) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	t_2 = t + (y * z)
	tmp = 0
	if y <= -1.02e+124:
		tmp = t_1
	elif y <= 2.95e-5:
		tmp = t_2
	elif y <= 5e+15:
		tmp = x * (y * y)
	elif y <= 8e+175:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * y))
	t_2 = Float64(t + Float64(y * z))
	tmp = 0.0
	if (y <= -1.02e+124)
		tmp = t_1;
	elseif (y <= 2.95e-5)
		tmp = t_2;
	elseif (y <= 5e+15)
		tmp = Float64(x * Float64(y * y));
	elseif (y <= 8e+175)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x * y);
	t_2 = t + (y * z);
	tmp = 0.0;
	if (y <= -1.02e+124)
		tmp = t_1;
	elseif (y <= 2.95e-5)
		tmp = t_2;
	elseif (y <= 5e+15)
		tmp = x * (y * y);
	elseif (y <= 8e+175)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e+124], t$95$1, If[LessEqual[y, 2.95e-5], t$95$2, If[LessEqual[y, 5e+15], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+175], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.01999999999999994e124 or 7.9999999999999995e175 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 98.4%

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

   3. Taylor expanded in y around inf 85.3%

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

      1. *-commutative 85.3%

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

      2. unpow2 85.3%

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

      3. associate-*r* 90.4%

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

      4. *-commutative 90.4%

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

      5. *-commutative 90.4%

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

   5. Simplified 90.4%

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

   if -1.01999999999999994e124 < y < 2.9499999999999999e-5 or 5e15 < y < 7.9999999999999995e175

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 82.7%

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

   if 2.9499999999999999e-5 < y < 5e15

   1. Initial program 99.6%

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

   2. Taylor expanded in t around 0 86.0%

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

   3. Taylor expanded in y around inf 85.5%

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

      1. *-commutative 85.5%

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

      2. unpow2 85.5%

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

   5. Simplified 85.5%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+124}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-5}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+175}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 3: 88.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+53} \lor \neg \left(y \leq 1.55 \cdot 10^{-81}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4e+53) (not (<= y 1.55e-81)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4e+53) || !(y <= 1.55e-81)) {
		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 <= (-4d+53)) .or. (.not. (y <= 1.55d-81))) 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 <= -4e+53) || !(y <= 1.55e-81)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4e+53) or not (y <= 1.55e-81):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4e+53) || !(y <= 1.55e-81))
		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 <= -4e+53) || ~((y <= 1.55e-81)))
		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, -4e+53], N[Not[LessEqual[y, 1.55e-81]], $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 < -4e53 or 1.54999999999999994e-81 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 89.1%

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

   if -4e53 < y < 1.54999999999999994e-81

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 91.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+53} \lor \neg \left(y \leq 1.55 \cdot 10^{-81}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 4: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+50} \lor \neg \left(y \leq 5.1 \cdot 10^{-79}\right):\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.2e+50) (not (<= y 5.1e-79))) (* x (* y y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e+50) || !(y <= 5.1e-79)) {
		tmp = x * (y * 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 <= (-4.2d+50)) .or. (.not. (y <= 5.1d-79))) then
        tmp = x * (y * 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 <= -4.2e+50) || !(y <= 5.1e-79)) {
		tmp = x * (y * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.2e+50) or not (y <= 5.1e-79):
		tmp = x * (y * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.2e+50) || !(y <= 5.1e-79))
		tmp = Float64(x * Float64(y * y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.2e+50) || ~((y <= 5.1e-79)))
		tmp = x * (y * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.2e+50], N[Not[LessEqual[y, 5.1e-79]], $MachinePrecision]], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999999e50 or 5.0999999999999999e-79 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 89.0%

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

   3. Taylor expanded in y around inf 65.4%

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

      1. *-commutative 65.4%

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

      2. unpow2 65.4%

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

   5. Simplified 65.4%

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

   if -4.1999999999999999e50 < y < 5.0999999999999999e-79

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 67.5%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+50} \lor \neg \left(y \leq 5.1 \cdot 10^{-79}\right):\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 64.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-79}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.8e+55) (* y (* x y)) (if (<= y 5.1e-79) t (* x (* y y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e+55) {
		tmp = y * (x * y);
	} else if (y <= 5.1e-79) {
		tmp = t;
	} else {
		tmp = x * (y * 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 <= (-6.8d+55)) then
        tmp = y * (x * y)
    else if (y <= 5.1d-79) then
        tmp = t
    else
        tmp = x * (y * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e+55) {
		tmp = y * (x * y);
	} else if (y <= 5.1e-79) {
		tmp = t;
	} else {
		tmp = x * (y * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.8e+55:
		tmp = y * (x * y)
	elif y <= 5.1e-79:
		tmp = t
	else:
		tmp = x * (y * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.8e+55)
		tmp = Float64(y * Float64(x * y));
	elseif (y <= 5.1e-79)
		tmp = t;
	else
		tmp = Float64(x * Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.8e+55)
		tmp = y * (x * y);
	elseif (y <= 5.1e-79)
		tmp = t;
	else
		tmp = x * (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.8e+55], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.1e-79], t, N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.7999999999999996e55

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 95.5%

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

   3. Taylor expanded in y around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. unpow2 71.6%

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

      3. associate-*r* 77.9%

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

      4. *-commutative 77.9%

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

      5. *-commutative 77.9%

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

   5. Simplified 77.9%

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

   if -6.7999999999999996e55 < y < 5.0999999999999999e-79

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 67.5%

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

   if 5.0999999999999999e-79 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 86.0%

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

   3. Taylor expanded in y around inf 62.5%

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

      1. *-commutative 62.5%

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

      2. unpow2 62.5%

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

   5. Simplified 62.5%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-79}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 6: 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 7: 51.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+132}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.25e+117) (* y z) (if (<= z 3.4e+132) t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e+117) {
		tmp = y * z;
	} else if (z <= 3.4e+132) {
		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 <= (-1.25d+117)) then
        tmp = y * z
    else if (z <= 3.4d+132) 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 <= -1.25e+117) {
		tmp = y * z;
	} else if (z <= 3.4e+132) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.25e+117:
		tmp = y * z
	elif z <= 3.4e+132:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.25e+117)
		tmp = Float64(y * z);
	elseif (z <= 3.4e+132)
		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 <= -1.25e+117)
		tmp = y * z;
	elseif (z <= 3.4e+132)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.25e+117], N[(y * z), $MachinePrecision], If[LessEqual[z, 3.4e+132], t, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.24999999999999996e117 or 3.40000000000000025e132 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.2%

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

   3. Taylor expanded in y around inf 64.4%

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

      1. *-commutative 64.4%

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

   5. Simplified 64.4%

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

   if -1.24999999999999996e117 < z < 3.40000000000000025e132

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 44.3%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+117}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+132}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 8: 38.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	return t
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 38.2%

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

3. Final simplification 38.2%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023176 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))