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

Percentage Accurate: 99.9% → 99.9%

Time: 8.9s

Alternatives: 8

Speedup: 1.0×

• 28.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-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. 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-17} \lor \neg \left(y \leq 4.9 \cdot 10^{-91}\right) \land \left(y \leq 17000000000000 \lor \neg \left(y \leq 1.3 \cdot 10^{+45}\right)\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.05e-17)
         (and (not (<= y 4.9e-91))
              (or (<= y 17000000000000.0) (not (<= y 1.3e+45)))))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e-17) || (!(y <= 4.9e-91) && ((y <= 17000000000000.0) || !(y <= 1.3e+45)))) {
		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 <= (-1.05d-17)) .or. (.not. (y <= 4.9d-91)) .and. (y <= 17000000000000.0d0) .or. (.not. (y <= 1.3d+45))) 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 <= -1.05e-17) || (!(y <= 4.9e-91) && ((y <= 17000000000000.0) || !(y <= 1.3e+45)))) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.05e-17) or (not (y <= 4.9e-91) and ((y <= 17000000000000.0) or not (y <= 1.3e+45))):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.05e-17) || (!(y <= 4.9e-91) && ((y <= 17000000000000.0) || !(y <= 1.3e+45))))
		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 <= -1.05e-17) || (~((y <= 4.9e-91)) && ((y <= 17000000000000.0) || ~((y <= 1.3e+45)))))
		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, -1.05e-17], And[N[Not[LessEqual[y, 4.9e-91]], $MachinePrecision], Or[LessEqual[y, 17000000000000.0], N[Not[LessEqual[y, 1.3e+45]], $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 < -1.04999999999999996e-17 or 4.8999999999999998e-91 < y < 1.7e13 or 1.30000000000000004e45 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 94.9%

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

      1. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in t around 0 87.8%

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

   7. Taylor expanded in z around 0 92.1%

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

      1. *-commutative 92.1%

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

   9. Simplified 92.1%

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

   if -1.04999999999999996e-17 < y < 4.8999999999999998e-91 or 1.7e13 < y < 1.30000000000000004e45

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.7%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-17} \lor \neg \left(y \leq 4.9 \cdot 10^{-91}\right) \land \left(y \leq 17000000000000 \lor \neg \left(y \leq 1.3 \cdot 10^{+45}\right)\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-91}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-25} \lor \neg \left(y \leq 1.6 \cdot 10^{+46}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ z (* x y)))))
   (if (<= y -1.05e-17)
     t_1
     (if (<= y 4.9e-91)
       (+ t (* y z))
       (if (or (<= y 2.1e-25) (not (<= y 1.6e+46)))
         t_1
         (+ t (* y (* x y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -1.05e-17) {
		tmp = t_1;
	} else if (y <= 4.9e-91) {
		tmp = t + (y * z);
	} else if ((y <= 2.1e-25) || !(y <= 1.6e+46)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z + (x * y))
    if (y <= (-1.05d-17)) then
        tmp = t_1
    else if (y <= 4.9d-91) then
        tmp = t + (y * z)
    else if ((y <= 2.1d-25) .or. (.not. (y <= 1.6d+46))) then
        tmp = t_1
    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 t_1 = y * (z + (x * y));
	double tmp;
	if (y <= -1.05e-17) {
		tmp = t_1;
	} else if (y <= 4.9e-91) {
		tmp = t + (y * z);
	} else if ((y <= 2.1e-25) || !(y <= 1.6e+46)) {
		tmp = t_1;
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z + (x * y))
	tmp = 0
	if y <= -1.05e-17:
		tmp = t_1
	elif y <= 4.9e-91:
		tmp = t + (y * z)
	elif (y <= 2.1e-25) or not (y <= 1.6e+46):
		tmp = t_1
	else:
		tmp = t + (y * (x * y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z + Float64(x * y)))
	tmp = 0.0
	if (y <= -1.05e-17)
		tmp = t_1;
	elseif (y <= 4.9e-91)
		tmp = Float64(t + Float64(y * z));
	elseif ((y <= 2.1e-25) || !(y <= 1.6e+46))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(y * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z + (x * y));
	tmp = 0.0;
	if (y <= -1.05e-17)
		tmp = t_1;
	elseif (y <= 4.9e-91)
		tmp = t + (y * z);
	elseif ((y <= 2.1e-25) || ~((y <= 1.6e+46)))
		tmp = t_1;
	else
		tmp = t + (y * (x * y));
	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, -1.05e-17], t$95$1, If[LessEqual[y, 4.9e-91], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.1e-25], N[Not[LessEqual[y, 1.6e+46]], $MachinePrecision]], t$95$1, N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04999999999999996e-17 or 4.8999999999999998e-91 < y < 2.10000000000000002e-25 or 1.5999999999999999e46 < 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 95.2%

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

      1. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in t around 0 89.7%

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

   7. Taylor expanded in z around 0 93.6%

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

      1. *-commutative 93.6%

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

   9. Simplified 93.6%

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

   if -1.04999999999999996e-17 < y < 4.8999999999999998e-91

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 96.3%

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

   if 2.10000000000000002e-25 < y < 1.5999999999999999e46

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 80.7%

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

      1. *-commutative 80.7%

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

   5. Simplified 80.7%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-91}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-25} \lor \neg \left(y \leq 1.6 \cdot 10^{+46}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-26} \lor \neg \left(y \leq 4.7 \cdot 10^{-91} \lor \neg \left(y \leq 8.5 \cdot 10^{+18}\right) \land y \leq 1.1 \cdot 10^{+42}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.5e-26)
         (not (or (<= y 4.7e-91) (and (not (<= y 8.5e+18)) (<= y 1.1e+42)))))
   (* y (* x y))
   t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e-26) || !((y <= 4.7e-91) || (!(y <= 8.5e+18) && (y <= 1.1e+42)))) {
		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 <= (-6.5d-26)) .or. (.not. (y <= 4.7d-91) .or. (.not. (y <= 8.5d+18)) .and. (y <= 1.1d+42))) 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 <= -6.5e-26) || !((y <= 4.7e-91) || (!(y <= 8.5e+18) && (y <= 1.1e+42)))) {
		tmp = y * (x * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.5e-26) or not ((y <= 4.7e-91) or (not (y <= 8.5e+18) and (y <= 1.1e+42))):
		tmp = y * (x * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.5e-26) || !((y <= 4.7e-91) || (!(y <= 8.5e+18) && (y <= 1.1e+42))))
		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 <= -6.5e-26) || ~(((y <= 4.7e-91) || (~((y <= 8.5e+18)) && (y <= 1.1e+42)))))
		tmp = y * (x * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.5e-26], N[Not[Or[LessEqual[y, 4.7e-91], And[N[Not[LessEqual[y, 8.5e+18]], $MachinePrecision], LessEqual[y, 1.1e+42]]]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e-26 or 4.70000000000000006e-91 < y < 8.5e18 or 1.1000000000000001e42 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 95.0%

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

      1. associate-/l* 90.6%

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

   5. Simplified 90.6%

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

   6. Taylor expanded in t around 0 87.4%

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

   7. Taylor expanded in z around 0 67.1%

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

      1. *-commutative 67.1%

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

   9. Simplified 67.1%

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

   if -6.5e-26 < y < 4.70000000000000006e-91 or 8.5e18 < y < 1.1000000000000001e42

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 66.5%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-26} \lor \neg \left(y \leq 4.7 \cdot 10^{-91} \lor \neg \left(y \leq 8.5 \cdot 10^{+18}\right) \land y \leq 1.1 \cdot 10^{+42}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+91} \lor \neg \left(y \leq 8.2 \cdot 10^{+48}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.25e+91) (not (<= y 8.2e+48))) (* y (* x y)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.25e+91) || !(y <= 8.2e+48)) {
		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 <= (-1.25d+91)) .or. (.not. (y <= 8.2d+48))) 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 <= -1.25e+91) || !(y <= 8.2e+48)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.25e+91) or not (y <= 8.2e+48):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.25e+91) || !(y <= 8.2e+48))
		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 <= -1.25e+91) || ~((y <= 8.2e+48)))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.25e+91], N[Not[LessEqual[y, 8.2e+48]], $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 < -1.2500000000000001e91 or 8.2000000000000005e48 < 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 98.9%

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

      1. associate-/l* 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in t around 0 94.9%

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

   7. Taylor expanded in z around 0 78.8%

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

      1. *-commutative 78.8%

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

   9. Simplified 78.8%

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

   if -1.2500000000000001e91 < y < 8.2000000000000005e48

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 82.0%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+91} \lor \neg \left(y \leq 8.2 \cdot 10^{+48}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+89} \lor \neg \left(z \leq 1.4 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.7e+89) (not (<= z 1.4e-5))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.7e+89) || !(z <= 1.4e-5)) {
		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 <= (-4.7d+89)) .or. (.not. (z <= 1.4d-5))) 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 <= -4.7e+89) || !(z <= 1.4e-5)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.7e+89) or not (z <= 1.4e-5):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.7e+89) || !(z <= 1.4e-5))
		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 <= -4.7e+89) || ~((z <= 1.4e-5)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.7e+89], N[Not[LessEqual[z, 1.4e-5]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -4.70000000000000022e89 or 1.39999999999999998e-5 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 66.5%

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

      1. +-commutative 66.5%

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

      2. +-commutative 66.5%

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

      3. unpow2 66.5%

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

      4. associate-/l* 65.1%

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

      5. distribute-lft-out 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in t around -inf 69.4%

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

      1. mul-1-neg 69.4%

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

      2. distribute-rgt-neg-in 69.4%

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

      3. fma-neg 69.4%

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

      4. associate-/l* 67.9%

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

      5. associate-/l* 65.9%

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

      6. associate-*r* 68.6%

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

      7. *-commutative 68.6%

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

      8. metadata-eval 68.6%

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

   8. Simplified 68.6%

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

   9. Taylor expanded in z around inf 57.6%

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

   if -4.70000000000000022e89 < z < 1.39999999999999998e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 42.5%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+89} \lor \neg \left(z \leq 1.4 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
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: 38.7% 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 33.2%

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

4. Final simplification 33.2%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024066 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))