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

Percentage Accurate: 99.9% → 99.9%

Time: 6.4s

Alternatives: 8

Speedup: 1.0×

• 28.1% 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, 1.0× speedup

Math

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

FPCore

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

C

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

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 * ((x * y) + z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 88.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+20} \lor \neg \left(z \leq 2 \cdot 10^{+64}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.5e+20) (not (<= z 2e+64)))
   (+ t (* y z))
   (+ t (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.5e+20) || !(z <= 2e+64)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.5d+20)) .or. (.not. (z <= 2d+64))) then
        tmp = t + (y * z)
    else
        tmp = t + (y * (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.5e+20) || !(z <= 2e+64)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.5e+20) or not (z <= 2e+64):
		tmp = t + (y * z)
	else:
		tmp = t + (y * (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.5e+20) || !(z <= 2e+64))
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(t + Float64(y * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.5e+20) || ~((z <= 2e+64)))
		tmp = t + (y * z);
	else
		tmp = t + (y * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.5e+20], N[Not[LessEqual[z, 2e+64]], $MachinePrecision]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e20 or 2.00000000000000004e64 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 86.5%

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

   if -6.5e20 < z < 2.00000000000000004e64

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 98.6%

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

      1. *-commutative 98.6%

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

   5. Simplified 98.6%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+20} \lor \neg \left(z \leq 2 \cdot 10^{+64}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+21} \lor \neg \left(z \leq 1.95 \cdot 10^{+64}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.2e+21) (not (<= z 1.95e+64)))
   (+ t (* y z))
   (+ t (* x (* y y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e+21) || !(z <= 1.95e+64)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (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 ((z <= (-2.2d+21)) .or. (.not. (z <= 1.95d+64))) then
        tmp = t + (y * z)
    else
        tmp = t + (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 ((z <= -2.2e+21) || !(z <= 1.95e+64)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (x * (y * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e+21) or not (z <= 1.95e+64):
		tmp = t + (y * z)
	else:
		tmp = t + (x * (y * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e+21) || !(z <= 1.95e+64))
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(t + Float64(x * Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.2e+21) || ~((z <= 1.95e+64)))
		tmp = t + (y * z);
	else
		tmp = t + (x * (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.2e+21], N[Not[LessEqual[z, 1.95e+64]], $MachinePrecision]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e21 or 1.9499999999999999e64 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 86.5%

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

   if -2.2e21 < z < 1.9499999999999999e64

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 92.8%

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

      1. +-commutative 92.8%

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

      2. unpow2 92.8%

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

      3. associate-/l* 93.5%

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

      4. distribute-lft-out 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in y around inf 94.9%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+21} \lor \neg \left(z \leq 1.95 \cdot 10^{+64}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+31} \lor \neg \left(y \leq 1.25 \cdot 10^{+78}\right):\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.4e+31) (not (<= y 1.25e+78)))
   (* y (+ (* x y) z))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.4e+31) || !(y <= 1.25e+78)) {
		tmp = y * ((x * y) + z);
	} 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 <= (-7.4d+31)) .or. (.not. (y <= 1.25d+78))) then
        tmp = y * ((x * y) + z)
    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 <= -7.4e+31) || !(y <= 1.25e+78)) {
		tmp = y * ((x * y) + z);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.4e+31) or not (y <= 1.25e+78):
		tmp = y * ((x * y) + z)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.4e+31) || !(y <= 1.25e+78))
		tmp = Float64(y * Float64(Float64(x * y) + z));
	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 <= -7.4e+31) || ~((y <= 1.25e+78)))
		tmp = y * ((x * y) + z);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.4e+31], N[Not[LessEqual[y, 1.25e+78]], $MachinePrecision]], N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.3999999999999996e31 or 1.24999999999999996e78 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 93.1%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{y \cdot \left(z + x \cdot y\right)}{t}\right)} \]
   4. Step-by-step derivation

      1. associate-/l* 93.1%

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

      2. +-commutative 93.1%

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

      3. *-commutative 93.1%

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

      4. fma-undefine 93.1%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{\mathsf{fma}\left(y, x, z\right)}}{t}\right) \]

   5. Simplified 93.1%

      \[\leadsto \color{blue}{t \cdot \left(1 + y \cdot \frac{\mathsf{fma}\left(y, x, z\right)}{t}\right)} \]

   6. Taylor expanded in t around 0 93.8%

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

   if -7.3999999999999996e31 < y < 1.24999999999999996e78

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.0%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+31} \lor \neg \left(y \leq 1.25 \cdot 10^{+78}\right):\\ \;\;\;\;y \cdot \left(x \cdot y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.48 \cdot 10^{+110} \lor \neg \left(y \leq 4.8 \cdot 10^{+79}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.48e+110) (not (<= y 4.8e+79))) (* y (* x y)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.48e+110) || !(y <= 4.8e+79)) {
		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 <= (-1.48d+110)) .or. (.not. (y <= 4.8d+79))) 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 <= -1.48e+110) || !(y <= 4.8e+79)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.48e+110) or not (y <= 4.8e+79):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.48e+110) || !(y <= 4.8e+79))
		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 <= -1.48e+110) || ~((y <= 4.8e+79)))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.48e+110], N[Not[LessEqual[y, 4.8e+79]], $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 < -1.48000000000000008e110 or 4.79999999999999971e79 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 96.0%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{y \cdot \left(z + x \cdot y\right)}{t}\right)} \]
   4. Step-by-step derivation

      1. associate-/l* 96.0%

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

      2. +-commutative 96.0%

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

      3. *-commutative 96.0%

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

      4. fma-undefine 96.0%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{\mathsf{fma}\left(y, x, z\right)}}{t}\right) \]

   5. Simplified 96.0%

      \[\leadsto \color{blue}{t \cdot \left(1 + y \cdot \frac{\mathsf{fma}\left(y, x, z\right)}{t}\right)} \]

   6. Taylor expanded in t around 0 96.9%

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

   7. Taylor expanded in z around 0 79.9%

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

   if -1.48000000000000008e110 < y < 4.79999999999999971e79

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 85.0%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.48 \cdot 10^{+110} \lor \neg \left(y \leq 4.8 \cdot 10^{+79}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+32} \lor \neg \left(y \leq 1.2 \cdot 10^{+40}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.9e+32) (not (<= y 1.2e+40))) (* y (* x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.9e+32) || !(y <= 1.2e+40)) {
		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 <= (-3.9d+32)) .or. (.not. (y <= 1.2d+40))) 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 <= -3.9e+32) || !(y <= 1.2e+40)) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.9e+32) or not (y <= 1.2e+40):
		tmp = y * (x * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.9e+32) || !(y <= 1.2e+40))
		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 <= -3.9e+32) || ~((y <= 1.2e+40)))
		tmp = y * (x * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.9e+32], N[Not[LessEqual[y, 1.2e+40]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -3.8999999999999999e32 or 1.2e40 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 93.5%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{y \cdot \left(z + x \cdot y\right)}{t}\right)} \]
   4. Step-by-step derivation

      1. associate-/l* 93.5%

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

      2. +-commutative 93.5%

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

      3. *-commutative 93.5%

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

      4. fma-undefine 93.5%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{\mathsf{fma}\left(y, x, z\right)}}{t}\right) \]

   5. Simplified 93.5%

      \[\leadsto \color{blue}{t \cdot \left(1 + y \cdot \frac{\mathsf{fma}\left(y, x, z\right)}{t}\right)} \]

   6. Taylor expanded in t around 0 92.4%

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

   7. Taylor expanded in z around 0 72.7%

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

   if -3.8999999999999999e32 < y < 1.2e40

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 64.5%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+32} \lor \neg \left(y \leq 1.2 \cdot 10^{+40}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+44} \lor \neg \left(z \leq 1.02 \cdot 10^{+63}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5e+44) (not (<= z 1.02e+63))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5e+44) || !(z <= 1.02e+63)) {
		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 <= (-5d+44)) .or. (.not. (z <= 1.02d+63))) 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 <= -5e+44) || !(z <= 1.02e+63)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5e+44) or not (z <= 1.02e+63):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5e+44) || !(z <= 1.02e+63))
		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 <= -5e+44) || ~((z <= 1.02e+63)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5e+44], N[Not[LessEqual[z, 1.02e+63]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999996e44 or 1.02e63 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 88.2%

      \[\leadsto \color{blue}{t \cdot \left(1 + \frac{y \cdot \left(z + x \cdot y\right)}{t}\right)} \]
   4. Step-by-step derivation

      1. associate-/l* 81.2%

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

      2. +-commutative 81.2%

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

      3. *-commutative 81.2%

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

      4. fma-undefine 81.2%

         \[\leadsto t \cdot \left(1 + y \cdot \frac{\color{blue}{\mathsf{fma}\left(y, x, z\right)}}{t}\right) \]

   5. Simplified 81.2%

      \[\leadsto \color{blue}{t \cdot \left(1 + y \cdot \frac{\mathsf{fma}\left(y, x, z\right)}{t}\right)} \]

   6. Taylor expanded in z around inf 61.1%

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

   if -4.9999999999999996e44 < z < 1.02e63

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 50.4%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+44} \lor \neg \left(z \leq 1.02 \cdot 10^{+63}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 39.8% 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 100.0%

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

3. Taylor expanded in y around 0 39.8%

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

Reproduce

herbie shell --seed 2024135 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))