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

Percentage Accurate: 99.9% → 99.9%

Time: 7.1s

Alternatives: 7

Speedup: 1.0×

• 29.3% 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

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

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 2: 63.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+121}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -1.25e+54)
     t_1
     (if (<= y 1e-33) t (if (<= y 2.05e+121) (* y z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -1.25e+54) {
		tmp = t_1;
	} else if (y <= 1e-33) {
		tmp = t;
	} else if (y <= 2.05e+121) {
		tmp = 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 * (x * y)
    if (y <= (-1.25d+54)) then
        tmp = t_1
    else if (y <= 1d-33) then
        tmp = t
    else if (y <= 2.05d+121) then
        tmp = 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 * (x * y);
	double tmp;
	if (y <= -1.25e+54) {
		tmp = t_1;
	} else if (y <= 1e-33) {
		tmp = t;
	} else if (y <= 2.05e+121) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	tmp = 0
	if y <= -1.25e+54:
		tmp = t_1
	elif y <= 1e-33:
		tmp = t
	elif y <= 2.05e+121:
		tmp = y * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * y))
	tmp = 0.0
	if (y <= -1.25e+54)
		tmp = t_1;
	elseif (y <= 1e-33)
		tmp = t;
	elseif (y <= 2.05e+121)
		tmp = Float64(y * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x * y);
	tmp = 0.0;
	if (y <= -1.25e+54)
		tmp = t_1;
	elseif (y <= 1e-33)
		tmp = t;
	elseif (y <= 2.05e+121)
		tmp = y * z;
	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]}, If[LessEqual[y, -1.25e+54], t$95$1, If[LessEqual[y, 1e-33], t, If[LessEqual[y, 2.05e+121], N[(y * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25000000000000001e54 or 2.05e121 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot y\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{x}\right)\right) \]

      6. *-lowering-*.f64 68.7%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right) \]

   5. Simplified 68.7%

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

   if -1.25000000000000001e54 < y < 1.0000000000000001e-33

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 63.3%

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

   if 1.0000000000000001e-33 < y < 2.05e121

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 51.7%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{z}\right) \]

   5. Simplified 51.7%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+121}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot z\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+67}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* y z))))
   (if (<= z -9.2e+107) t_1 (if (<= z 4e+67) (+ t (* y (* x y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + (y * z);
	double tmp;
	if (z <= -9.2e+107) {
		tmp = t_1;
	} else if (z <= 4e+67) {
		tmp = t + (y * (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + (y * z)
    if (z <= (-9.2d+107)) then
        tmp = t_1
    else if (z <= 4d+67) then
        tmp = t + (y * (x * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t + (y * z);
	double tmp;
	if (z <= -9.2e+107) {
		tmp = t_1;
	} else if (z <= 4e+67) {
		tmp = t + (y * (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + (y * z)
	tmp = 0
	if z <= -9.2e+107:
		tmp = t_1
	elif z <= 4e+67:
		tmp = t + (y * (x * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(y * z))
	tmp = 0.0
	if (z <= -9.2e+107)
		tmp = t_1;
	elseif (z <= 4e+67)
		tmp = Float64(t + Float64(y * Float64(x * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + (y * z);
	tmp = 0.0;
	if (z <= -9.2e+107)
		tmp = t_1;
	elseif (z <= 4e+67)
		tmp = t + (y * (x * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e+107], t$95$1, If[LessEqual[z, 4e+67], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2000000000000001e107 or 3.99999999999999993e67 < 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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{z}, y\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 94.1%

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

   if -9.2000000000000001e107 < z < 3.99999999999999993e67

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(x \cdot y\right)}, y\right), t\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y \cdot x\right), y\right), t\right) \]

      2. *-lowering-*.f64 90.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 90.4%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+107}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+67}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-30}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))))
   (if (<= y -6e+55) t_1 (if (<= y 1.02e-30) (+ 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 <= -6e+55) {
		tmp = t_1;
	} else if (y <= 1.02e-30) {
		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 <= (-6d+55)) then
        tmp = t_1
    else if (y <= 1.02d-30) 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 <= -6e+55) {
		tmp = t_1;
	} else if (y <= 1.02e-30) {
		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 <= -6e+55:
		tmp = t_1
	elif y <= 1.02e-30:
		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 <= -6e+55)
		tmp = t_1;
	elseif (y <= 1.02e-30)
		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 <= -6e+55)
		tmp = t_1;
	elseif (y <= 1.02e-30)
		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, -6e+55], t$95$1, If[LessEqual[y, 1.02e-30], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.00000000000000033e55 or 1.0199999999999999e-30 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. distribute-rgt-in N/A

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

      2. +-commutative N/A

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

      3. unpow2 N/A

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

      4. associate-*r* N/A

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

      5. fma-define N/A

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

      6. associate-*l/ N/A

         \[\leadsto \mathsf{fma}\left(\frac{z \cdot y}{y}, y, x \cdot {y}^{2}\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{fma}\left(z \cdot \frac{y}{y}, y, x \cdot {y}^{2}\right) \]

      8. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(z \cdot 1, y, x \cdot {y}^{2}\right) \]

      9. *-rgt-identity N/A

         \[\leadsto \mathsf{fma}\left(z, y, x \cdot {y}^{2}\right) \]

      10. fma-define N/A

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

      11. *-commutative N/A

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

      12. unpow2 N/A

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

      13. associate-*r* N/A

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

      14. *-commutative N/A

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

      15. distribute-lft-in N/A

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

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(z + x \cdot y\right)}\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \left(y \cdot \color{blue}{x}\right)\right)\right) \]

      19. *-lowering-*.f64 93.0%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 93.0%

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

   if -6.00000000000000033e55 < y < 1.0199999999999999e-30

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{z}, y\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 87.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-30}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+121}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -3.4e+75) t_1 (if (<= y 8.5e+121) (+ t (* y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -3.4e+75) {
		tmp = t_1;
	} else if (y <= 8.5e+121) {
		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 * (x * y)
    if (y <= (-3.4d+75)) then
        tmp = t_1
    else if (y <= 8.5d+121) 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 * (x * y);
	double tmp;
	if (y <= -3.4e+75) {
		tmp = t_1;
	} else if (y <= 8.5e+121) {
		tmp = t + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	tmp = 0
	if y <= -3.4e+75:
		tmp = t_1
	elif y <= 8.5e+121:
		tmp = t + (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * y))
	tmp = 0.0
	if (y <= -3.4e+75)
		tmp = t_1;
	elseif (y <= 8.5e+121)
		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 * (x * y);
	tmp = 0.0;
	if (y <= -3.4e+75)
		tmp = t_1;
	elseif (y <= 8.5e+121)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+75], t$95$1, If[LessEqual[y, 8.5e+121], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.40000000000000011e75 or 8.5e121 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot y\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(y \cdot \color{blue}{x}\right)\right) \]

      6. *-lowering-*.f64 70.6%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right) \]

   5. Simplified 70.6%

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

   if -3.40000000000000011e75 < y < 8.5e121

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{z}, y\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 83.8%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+75}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+121}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+55}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-37}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.5e+55) (* y z) (if (<= y 3.8e-37) t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+55) {
		tmp = y * z;
	} else if (y <= 3.8e-37) {
		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 (y <= (-1.5d+55)) then
        tmp = y * z
    else if (y <= 3.8d-37) 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 (y <= -1.5e+55) {
		tmp = y * z;
	} else if (y <= 3.8e-37) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.5e+55:
		tmp = y * z
	elif y <= 3.8e-37:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.5e+55)
		tmp = Float64(y * z);
	elseif (y <= 3.8e-37)
		tmp = t;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.5e+55)
		tmp = y * z;
	elseif (y <= 3.8e-37)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.5e+55], N[(y * z), $MachinePrecision], If[LessEqual[y, 3.8e-37], t, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000008e55 or 3.8000000000000004e-37 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 40.5%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{z}\right) \]

   5. Simplified 40.5%

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

   if -1.50000000000000008e55 < y < 3.8000000000000004e-37

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 63.3%

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

Alternative 7: 38.6% 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

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Simplified 37.9%

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

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))