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

Percentage Accurate: 99.9% → 99.9%

Time: 7.9s

Alternatives: 8

Speedup: 1.0×

• 29.6% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 99.9%

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

   1. +-commutative 99.9%

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

   2. *-commutative 99.9%

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

   3. fma-undefine 99.9%

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

5. Simplified 99.9%

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

6. Final simplification 99.9%

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

Alternative 2: 88.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot z\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-8}:\\ \;\;\;\;t + y \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(z + y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* y z))))
   (if (<= z -6.2e+42)
     t_1
     (if (<= z 2.7e-8)
       (+ t (* y (* y x)))
       (if (<= z 9.5e+121) (* y (+ z (* y x))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + (y * z);
	double tmp;
	if (z <= -6.2e+42) {
		tmp = t_1;
	} else if (z <= 2.7e-8) {
		tmp = t + (y * (y * x));
	} else if (z <= 9.5e+121) {
		tmp = y * (z + (y * x));
	} 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 <= (-6.2d+42)) then
        tmp = t_1
    else if (z <= 2.7d-8) then
        tmp = t + (y * (y * x))
    else if (z <= 9.5d+121) then
        tmp = y * (z + (y * x))
    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 <= -6.2e+42) {
		tmp = t_1;
	} else if (z <= 2.7e-8) {
		tmp = t + (y * (y * x));
	} else if (z <= 9.5e+121) {
		tmp = y * (z + (y * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + (y * z)
	tmp = 0
	if z <= -6.2e+42:
		tmp = t_1
	elif z <= 2.7e-8:
		tmp = t + (y * (y * x))
	elif z <= 9.5e+121:
		tmp = y * (z + (y * x))
	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 <= -6.2e+42)
		tmp = t_1;
	elseif (z <= 2.7e-8)
		tmp = Float64(t + Float64(y * Float64(y * x)));
	elseif (z <= 9.5e+121)
		tmp = Float64(y * Float64(z + Float64(y * x)));
	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 <= -6.2e+42)
		tmp = t_1;
	elseif (z <= 2.7e-8)
		tmp = t + (y * (y * x));
	elseif (z <= 9.5e+121)
		tmp = y * (z + (y * x));
	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, -6.2e+42], t$95$1, If[LessEqual[z, 2.7e-8], N[(t + N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+121], N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2000000000000003e42 or 9.49999999999999949e121 < 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 92.6%

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

   if -6.2000000000000003e42 < z < 2.70000000000000002e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 97.7%

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

      1. *-commutative 97.7%

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

   5. Simplified 97.7%

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

   if 2.70000000000000002e-8 < z < 9.49999999999999949e121

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 90.5%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+42}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-8}:\\ \;\;\;\;t + y \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(z + y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+24} \lor \neg \left(y \leq 4.6 \cdot 10^{+59}\right):\\ \;\;\;\;y \cdot \left(z + y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.8e+24) (not (<= y 4.6e+59)))
   (* y (+ z (* y x)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.8e+24) || !(y <= 4.6e+59)) {
		tmp = y * (z + (y * x));
	} 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 <= (-6.8d+24)) .or. (.not. (y <= 4.6d+59))) then
        tmp = y * (z + (y * x))
    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 <= -6.8e+24) || !(y <= 4.6e+59)) {
		tmp = y * (z + (y * x));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.8e+24) or not (y <= 4.6e+59):
		tmp = y * (z + (y * x))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.8e+24) || !(y <= 4.6e+59))
		tmp = Float64(y * Float64(z + Float64(y * x)));
	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 <= -6.8e+24) || ~((y <= 4.6e+59)))
		tmp = y * (z + (y * x));
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.8e+24], N[Not[LessEqual[y, 4.6e+59]], $MachinePrecision]], N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8000000000000001e24 or 4.60000000000000016e59 < 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 93.8%

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

   if -6.8000000000000001e24 < y < 4.60000000000000016e59

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 87.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+24} \lor \neg \left(y \leq 4.6 \cdot 10^{+59}\right):\\ \;\;\;\;y \cdot \left(z + y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+24} \lor \neg \left(y \leq 1.05 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.8e+24) (not (<= y 1.05e+65))) (* y (* y x)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.8e+24) || !(y <= 1.05e+65)) {
		tmp = y * (y * x);
	} 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 <= (-6.8d+24)) .or. (.not. (y <= 1.05d+65))) then
        tmp = y * (y * x)
    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 <= -6.8e+24) || !(y <= 1.05e+65)) {
		tmp = y * (y * x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.8e+24) or not (y <= 1.05e+65):
		tmp = y * (y * x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.8e+24) || !(y <= 1.05e+65))
		tmp = Float64(y * Float64(y * x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.8e+24) || ~((y <= 1.05e+65)))
		tmp = y * (y * x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.8e+24], N[Not[LessEqual[y, 1.05e+65]], $MachinePrecision]], N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -6.8000000000000001e24 or 1.04999999999999996e65 < 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 93.8%

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

   4. Taylor expanded in z around 0 68.0%

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

      1. *-commutative 68.0%

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

   6. Simplified 68.0%

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

   if -6.8000000000000001e24 < y < 1.04999999999999996e65

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 63.3%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+24} \lor \neg \left(y \leq 1.05 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+105} \lor \neg \left(y \leq 1.25 \cdot 10^{+98}\right):\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.7e+105) (not (<= y 1.25e+98))) (* y (* y x)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.7e+105) || !(y <= 1.25e+98)) {
		tmp = y * (y * x);
	} 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 <= (-2.7d+105)) .or. (.not. (y <= 1.25d+98))) then
        tmp = y * (y * x)
    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 <= -2.7e+105) || !(y <= 1.25e+98)) {
		tmp = y * (y * x);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.7e+105) or not (y <= 1.25e+98):
		tmp = y * (y * x)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.7e+105) || !(y <= 1.25e+98))
		tmp = Float64(y * Float64(y * x));
	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 <= -2.7e+105) || ~((y <= 1.25e+98)))
		tmp = y * (y * x);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.7e+105], N[Not[LessEqual[y, 1.25e+98]], $MachinePrecision]], N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.70000000000000016e105 or 1.25e98 < 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 97.6%

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

   4. Taylor expanded in z around 0 75.9%

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

      1. *-commutative 75.9%

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

   6. Simplified 75.9%

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

   if -2.70000000000000016e105 < y < 1.25e98

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 81.8%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+105} \lor \neg \left(y \leq 1.25 \cdot 10^{+98}\right):\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+52} \lor \neg \left(z \leq 4.6 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e+52) (not (<= z 4.6e+16))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e+52) || !(z <= 4.6e+16)) {
		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+52)) .or. (.not. (z <= 4.6d+16))) 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+52) || !(z <= 4.6e+16)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e+52) or not (z <= 4.6e+16):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.8e+52) || !(z <= 4.6e+16))
		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+52) || ~((z <= 4.6e+16)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.8e+52], N[Not[LessEqual[z, 4.6e+16]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e52 or 4.6e16 < 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 79.8%

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

   4. Taylor expanded in z around inf 64.1%

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

   if -2.8e52 < z < 4.6e16

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 49.4%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+52} \lor \neg \left(z \leq 4.6 \cdot 10^{+16}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (y * x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   \[\leadsto t + y \cdot \left(z + y \cdot x\right) \]
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 36.4%

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

4. Final simplification 36.4%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))