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

Percentage Accurate: 99.9% → 99.9%

Time: 8.2s

Alternatives: 8

Speedup: 1.0×

• 29.8% 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-def 99.9%

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

   2. fma-def 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 87.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+23} \lor \neg \left(y \leq -8.5 \cdot 10^{-122} \lor \neg \left(y \leq -1 \cdot 10^{-144}\right) \land y \leq 1.12 \cdot 10^{+30}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.9e+23)
         (not
          (or (<= y -8.5e-122) (and (not (<= y -1e-144)) (<= y 1.12e+30)))))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e+23) || !((y <= -8.5e-122) || (!(y <= -1e-144) && (y <= 1.12e+30)))) {
		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 <= (-1.9d+23)) .or. (.not. (y <= (-8.5d-122)) .or. (.not. (y <= (-1d-144))) .and. (y <= 1.12d+30))) 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 <= -1.9e+23) || !((y <= -8.5e-122) || (!(y <= -1e-144) && (y <= 1.12e+30)))) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.9e+23) or not ((y <= -8.5e-122) or (not (y <= -1e-144) and (y <= 1.12e+30))):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.9e+23) || !((y <= -8.5e-122) || (!(y <= -1e-144) && (y <= 1.12e+30))))
		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 <= -1.9e+23) || ~(((y <= -8.5e-122) || (~((y <= -1e-144)) && (y <= 1.12e+30)))))
		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, -1.9e+23], N[Not[Or[LessEqual[y, -8.5e-122], And[N[Not[LessEqual[y, -1e-144]], $MachinePrecision], LessEqual[y, 1.12e+30]]]], $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 < -1.89999999999999987e23 or -8.50000000000000003e-122 < y < -9.9999999999999995e-145 or 1.12e30 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 92.5%

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

   if -1.89999999999999987e23 < y < -8.50000000000000003e-122 or -9.9999999999999995e-145 < y < 1.12e30

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 89.1%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+23} \lor \neg \left(y \leq -8.5 \cdot 10^{-122} \lor \neg \left(y \leq -1 \cdot 10^{-144}\right) \land y \leq 1.12 \cdot 10^{+30}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1850 \lor \neg \left(y \leq -8.5 \cdot 10^{-122} \lor \neg \left(y \leq -4.8 \cdot 10^{-145}\right) \land y \leq 1.65 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1850.0)
         (not
          (or (<= y -8.5e-122) (and (not (<= y -4.8e-145)) (<= y 1.65e+31)))))
   (* y (* x y))
   t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1850.0) || !((y <= -8.5e-122) || (!(y <= -4.8e-145) && (y <= 1.65e+31)))) {
		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 <= (-1850.0d0)) .or. (.not. (y <= (-8.5d-122)) .or. (.not. (y <= (-4.8d-145))) .and. (y <= 1.65d+31))) 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 <= -1850.0) || !((y <= -8.5e-122) || (!(y <= -4.8e-145) && (y <= 1.65e+31)))) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1850.0) or not ((y <= -8.5e-122) or (not (y <= -4.8e-145) and (y <= 1.65e+31))):
		tmp = y * (x * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1850.0) || !((y <= -8.5e-122) || (!(y <= -4.8e-145) && (y <= 1.65e+31))))
		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 <= -1850.0) || ~(((y <= -8.5e-122) || (~((y <= -4.8e-145)) && (y <= 1.65e+31)))))
		tmp = y * (x * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1850.0], N[Not[Or[LessEqual[y, -8.5e-122], And[N[Not[LessEqual[y, -4.8e-145]], $MachinePrecision], LessEqual[y, 1.65e+31]]]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -1850 or -8.50000000000000003e-122 < y < -4.8000000000000003e-145 or 1.64999999999999996e31 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 92.0%

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

   4. Taylor expanded in z around 0 71.6%

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

      1. *-commutative 71.6%

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

   6. Simplified 71.6%

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

   if -1850 < y < -8.50000000000000003e-122 or -4.8000000000000003e-145 < y < 1.64999999999999996e31

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 66.3%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1850 \lor \neg \left(y \leq -8.5 \cdot 10^{-122} \lor \neg \left(y \leq -4.8 \cdot 10^{-145}\right) \land y \leq 1.65 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+57} \lor \neg \left(y \leq -8.5 \cdot 10^{-122} \lor \neg \left(y \leq -1 \cdot 10^{-144}\right) \land y \leq 8.5 \cdot 10^{+78}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.8e+57)
         (not (or (<= y -8.5e-122) (and (not (<= y -1e-144)) (<= y 8.5e+78)))))
   (* y (* x y))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.8e+57) || !((y <= -8.5e-122) || (!(y <= -1e-144) && (y <= 8.5e+78)))) {
		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 <= (-5.8d+57)) .or. (.not. (y <= (-8.5d-122)) .or. (.not. (y <= (-1d-144))) .and. (y <= 8.5d+78))) 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 <= -5.8e+57) || !((y <= -8.5e-122) || (!(y <= -1e-144) && (y <= 8.5e+78)))) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.8e+57) or not ((y <= -8.5e-122) or (not (y <= -1e-144) and (y <= 8.5e+78))):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.8e+57) || !((y <= -8.5e-122) || (!(y <= -1e-144) && (y <= 8.5e+78))))
		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 <= -5.8e+57) || ~(((y <= -8.5e-122) || (~((y <= -1e-144)) && (y <= 8.5e+78)))))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.8e+57], N[Not[Or[LessEqual[y, -8.5e-122], And[N[Not[LessEqual[y, -1e-144]], $MachinePrecision], LessEqual[y, 8.5e+78]]]], $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 < -5.8000000000000003e57 or -8.50000000000000003e-122 < y < -9.9999999999999995e-145 or 8.50000000000000079e78 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 93.0%

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

   4. Taylor expanded in z around 0 77.1%

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

      1. *-commutative 77.1%

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

   6. Simplified 77.1%

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

   if -5.8000000000000003e57 < y < -8.50000000000000003e-122 or -9.9999999999999995e-145 < y < 8.50000000000000079e78

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]
   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 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+57} \lor \neg \left(y \leq -8.5 \cdot 10^{-122} \lor \neg \left(y \leq -1 \cdot 10^{-144}\right) \land y \leq 8.5 \cdot 10^{+78}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+102}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;z \leq 0.36:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.9e+102)
   (+ t (* y z))
   (if (<= z 0.36) (+ t (* y (* x y))) (* y (+ z (* x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e+102) {
		tmp = t + (y * z);
	} else if (z <= 0.36) {
		tmp = t + (y * (x * y));
	} else {
		tmp = y * (z + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.9d+102)) then
        tmp = t + (y * z)
    else if (z <= 0.36d0) then
        tmp = t + (y * (x * y))
    else
        tmp = y * (z + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e+102) {
		tmp = t + (y * z);
	} else if (z <= 0.36) {
		tmp = t + (y * (x * y));
	} else {
		tmp = y * (z + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.9e+102:
		tmp = t + (y * z)
	elif z <= 0.36:
		tmp = t + (y * (x * y))
	else:
		tmp = y * (z + (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.9e+102)
		tmp = Float64(t + Float64(y * z));
	elseif (z <= 0.36)
		tmp = Float64(t + Float64(y * Float64(x * y)));
	else
		tmp = Float64(y * Float64(z + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.9e+102)
		tmp = t + (y * z);
	elseif (z <= 0.36)
		tmp = t + (y * (x * y));
	else
		tmp = y * (z + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.9e+102], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.36], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9000000000000002e102

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.8%

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

   if -2.9000000000000002e102 < z < 0.35999999999999999

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 95.0%

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

      1. *-commutative 95.0%

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

   5. Simplified 95.0%

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

   if 0.35999999999999999 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 81.6%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+102}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;z \leq 0.36:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+102} \lor \neg \left(z \leq 0.36\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e+102) (not (<= z 0.36))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e+102) || !(z <= 0.36)) {
		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 <= (-2.8d+102)) .or. (.not. (z <= 0.36d0))) 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 <= -2.8e+102) || !(z <= 0.36)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e+102) or not (z <= 0.36):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.8e+102) || !(z <= 0.36))
		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 <= -2.8e+102) || ~((z <= 0.36)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.8e+102], N[Not[LessEqual[z, 0.36]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -2.80000000000000018e102 or 0.35999999999999999 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 79.4%

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

   4. Taylor expanded in z around inf 61.2%

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

   if -2.80000000000000018e102 < z < 0.35999999999999999

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 42.0%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+102} \lor \neg \left(z \leq 0.36\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
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: 38.0% 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 34.4%

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

4. Final simplification 34.4%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024027 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))