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

Percentage Accurate: 99.9% → 99.9%

Time: 8.8s

Alternatives: 8

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-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: 89.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-22}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 40000000:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))))
   (if (<= y -2.4e+62)
     t_1
     (if (<= y -2.7e-22)
       (+ t (* y (* x y)))
       (if (<= y 40000000.0) (+ t (* y z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -2.4e+62) {
		tmp = t_1;
	} else if (y <= -2.7e-22) {
		tmp = t + (y * (x * y));
	} else if (y <= 40000000.0) {
		tmp = t + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z + (x * y))
    if (y <= (-2.4d+62)) then
        tmp = t_1
    else if (y <= (-2.7d-22)) then
        tmp = t + (y * (x * y))
    else if (y <= 40000000.0d0) then
        tmp = t + (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -2.4e+62) {
		tmp = t_1;
	} else if (y <= -2.7e-22) {
		tmp = t + (y * (x * y));
	} else if (y <= 40000000.0) {
		tmp = t + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z + (x * y))
	tmp = 0
	if y <= -2.4e+62:
		tmp = t_1
	elif y <= -2.7e-22:
		tmp = t + (y * (x * y))
	elif y <= 40000000.0:
		tmp = t + (y * z)
	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 <= -2.4e+62)
		tmp = t_1;
	elseif (y <= -2.7e-22)
		tmp = Float64(t + Float64(y * Float64(x * y)));
	elseif (y <= 40000000.0)
		tmp = Float64(t + Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z + (x * y));
	tmp = 0.0;
	if (y <= -2.4e+62)
		tmp = t_1;
	elseif (y <= -2.7e-22)
		tmp = t + (y * (x * y));
	elseif (y <= 40000000.0)
		tmp = t + (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+62], t$95$1, If[LessEqual[y, -2.7e-22], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 40000000.0], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4e62 or 4e7 < y

   1. Initial program 99.9%

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

      1. fma-define 99.9%

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

      2. add-cube-cbrt 99.5%

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

      3. associate-*l* 99.5%

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

      4. fma-define 99.5%

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

      5. pow2 99.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z\right)}\right)}^{2}}, \sqrt[3]{\mathsf{fma}\left(x, y, z\right)} \cdot y, t\right) \]

   4. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\mathsf{fma}\left(x, y, z\right)}\right)}^{2}, \sqrt[3]{\mathsf{fma}\left(x, y, z\right)} \cdot y, t\right)} \]

   5. Taylor expanded in t around 0 92.7%

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

   if -2.4e62 < y < -2.7000000000000002e-22

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 94.5%

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

      1. *-commutative 94.5%

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

   5. Simplified 94.5%

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

   if -2.7000000000000002e-22 < y < 4e7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 93.7%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+62}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-22}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 40000000:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-40} \lor \neg \left(y \leq 370\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.45e-40) (not (<= y 370.0)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.45e-40) || !(y <= 370.0)) {
		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 <= (-1.45d-40)) .or. (.not. (y <= 370.0d0))) 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 <= -1.45e-40) || !(y <= 370.0)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.45e-40) or not (y <= 370.0):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.45e-40) || !(y <= 370.0))
		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 <= -1.45e-40) || ~((y <= 370.0)))
		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, -1.45e-40], N[Not[LessEqual[y, 370.0]], $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 < -1.4499999999999999e-40 or 370 < y

   1. Initial program 99.9%

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

      1. fma-define 99.9%

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

      2. add-cube-cbrt 99.4%

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

      3. associate-*l* 99.4%

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

      4. fma-define 99.4%

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

      5. pow2 99.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z\right)}\right)}^{2}}, \sqrt[3]{\mathsf{fma}\left(x, y, z\right)} \cdot y, t\right) \]

   4. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\mathsf{fma}\left(x, y, z\right)}\right)}^{2}, \sqrt[3]{\mathsf{fma}\left(x, y, z\right)} \cdot y, t\right)} \]

   5. Taylor expanded in t around 0 87.2%

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

   if -1.4499999999999999e-40 < y < 370

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-40} \lor \neg \left(y \leq 370\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+68} \lor \neg \left(y \leq 6.2 \cdot 10^{+75}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8e+68) (not (<= y 6.2e+75))) (* y (* x y)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e+68) || !(y <= 6.2e+75)) {
		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 <= (-8d+68)) .or. (.not. (y <= 6.2d+75))) 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 <= -8e+68) || !(y <= 6.2e+75)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8e+68) or not (y <= 6.2e+75):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8e+68) || !(y <= 6.2e+75))
		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 <= -8e+68) || ~((y <= 6.2e+75)))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8e+68], N[Not[LessEqual[y, 6.2e+75]], $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 < -7.99999999999999962e68 or 6.2000000000000002e75 < y

   1. Initial program 99.9%

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

      1. fma-define 99.9%

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

      2. add-cube-cbrt 99.6%

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

      3. associate-*l* 99.6%

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

      4. fma-define 99.6%

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

      5. pow2 99.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z\right)}\right)}^{2}}, \sqrt[3]{\mathsf{fma}\left(x, y, z\right)} \cdot y, t\right) \]

   4. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\mathsf{fma}\left(x, y, z\right)}\right)}^{2}, \sqrt[3]{\mathsf{fma}\left(x, y, z\right)} \cdot y, t\right)} \]

   5. Taylor expanded in t around 0 93.9%

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

   6. Taylor expanded in z around 0 77.9%

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

      1. *-commutative 77.9%

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

   8. Simplified 77.9%

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

   if -7.99999999999999962e68 < y < 6.2000000000000002e75

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 87.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+68} \lor \neg \left(y \leq 6.2 \cdot 10^{+75}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-40} \lor \neg \left(y \leq 1.92\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.35e-40) (not (<= y 1.92))) (* y (* x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.35e-40) || !(y <= 1.92)) {
		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 <= (-1.35d-40)) .or. (.not. (y <= 1.92d0))) 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 <= -1.35e-40) || !(y <= 1.92)) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.35e-40) or not (y <= 1.92):
		tmp = y * (x * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.35e-40) || !(y <= 1.92))
		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 <= -1.35e-40) || ~((y <= 1.92)))
		tmp = y * (x * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.35e-40], N[Not[LessEqual[y, 1.92]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e-40 or 1.9199999999999999 < y

   1. Initial program 99.9%

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

      1. fma-define 99.9%

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

      2. add-cube-cbrt 99.4%

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

      3. associate-*l* 99.4%

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

      4. fma-define 99.4%

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

      5. pow2 99.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z\right)}\right)}^{2}}, \sqrt[3]{\mathsf{fma}\left(x, y, z\right)} \cdot y, t\right) \]

   4. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\mathsf{fma}\left(x, y, z\right)}\right)}^{2}, \sqrt[3]{\mathsf{fma}\left(x, y, z\right)} \cdot y, t\right)} \]

   5. Taylor expanded in t around 0 87.2%

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

   6. Taylor expanded in z around 0 70.3%

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

      1. *-commutative 70.3%

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

   8. Simplified 70.3%

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

   if -1.35e-40 < y < 1.9199999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 68.7%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-40} \lor \neg \left(y \leq 1.92\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+105} \lor \neg \left(z \leq 6 \cdot 10^{+54}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.3e+105) (not (<= z 6e+54))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.3e+105) || !(z <= 6e+54)) {
		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 <= (-2.3d+105)) .or. (.not. (z <= 6d+54))) 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 <= -2.3e+105) || !(z <= 6e+54)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.3e+105) or not (z <= 6e+54):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.3e+105) || !(z <= 6e+54))
		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 <= -2.3e+105) || ~((z <= 6e+54)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.3e+105], N[Not[LessEqual[z, 6e+54]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999998e105 or 5.9999999999999998e54 < z

   1. Initial program 99.9%

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

      1. fma-define 99.9%

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

      2. add-cube-cbrt 99.1%

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

      3. associate-*l* 99.1%

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

      4. fma-define 99.1%

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

      5. pow2 99.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, z\right)}\right)}^{2}}, \sqrt[3]{\mathsf{fma}\left(x, y, z\right)} \cdot y, t\right) \]

   4. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\mathsf{fma}\left(x, y, z\right)}\right)}^{2}, \sqrt[3]{\mathsf{fma}\left(x, y, z\right)} \cdot y, t\right)} \]

   5. Taylor expanded in z around inf 62.8%

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

      1. *-commutative 62.8%

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

   7. Simplified 62.8%

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

   if -2.2999999999999998e105 < z < 5.9999999999999998e54

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 54.8%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+105} \lor \neg \left(z \leq 6 \cdot 10^{+54}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 8: 37.7% 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 41.1%

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

Reproduce

herbie shell --seed 2024091 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))