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

Percentage Accurate: 99.9% → 99.9%

Time: 6.8s

Alternatives: 7

Speedup: 1.0×

• 29.0% 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 100.0%

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

3. Taylor expanded in x around 0 100.0%

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

   1. +-commutative 100.0%

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

   2. *-commutative 100.0%

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

   3. fma-udef 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 64.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+73}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+41} \lor \neg \left(y \leq 4.8 \cdot 10^{-21}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* y x))))
   (if (<= y -1.12e+105)
     t_1
     (if (<= y -4.6e+73)
       (* y z)
       (if (or (<= y -1.25e+41) (not (<= y 4.8e-21))) t_1 t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (y * x);
	double tmp;
	if (y <= -1.12e+105) {
		tmp = t_1;
	} else if (y <= -4.6e+73) {
		tmp = y * z;
	} else if ((y <= -1.25e+41) || !(y <= 4.8e-21)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (y * x)
    if (y <= (-1.12d+105)) then
        tmp = t_1
    else if (y <= (-4.6d+73)) then
        tmp = y * z
    else if ((y <= (-1.25d+41)) .or. (.not. (y <= 4.8d-21))) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (y * x);
	double tmp;
	if (y <= -1.12e+105) {
		tmp = t_1;
	} else if (y <= -4.6e+73) {
		tmp = y * z;
	} else if ((y <= -1.25e+41) || !(y <= 4.8e-21)) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (y * x)
	tmp = 0
	if y <= -1.12e+105:
		tmp = t_1
	elif y <= -4.6e+73:
		tmp = y * z
	elif (y <= -1.25e+41) or not (y <= 4.8e-21):
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(y * x))
	tmp = 0.0
	if (y <= -1.12e+105)
		tmp = t_1;
	elseif (y <= -4.6e+73)
		tmp = Float64(y * z);
	elseif ((y <= -1.25e+41) || !(y <= 4.8e-21))
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (y * x);
	tmp = 0.0;
	if (y <= -1.12e+105)
		tmp = t_1;
	elseif (y <= -4.6e+73)
		tmp = y * z;
	elseif ((y <= -1.25e+41) || ~((y <= 4.8e-21)))
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+105], t$95$1, If[LessEqual[y, -4.6e+73], N[(y * z), $MachinePrecision], If[Or[LessEqual[y, -1.25e+41], N[Not[LessEqual[y, 4.8e-21]], $MachinePrecision]], t$95$1, t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12e105 or -4.6e73 < y < -1.25000000000000006e41 or 4.7999999999999999e-21 < y

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 94.9%

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

   6. Taylor expanded in z around 0 78.3%

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

      1. *-commutative 78.3%

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

   8. Simplified 78.3%

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

   if -1.12e105 < y < -4.6e73

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 90.7%

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

   6. Taylor expanded in z around inf 70.7%

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

   if -1.25000000000000006e41 < y < 4.7999999999999999e-21

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 71.8%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+73}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+41} \lor \neg \left(y \leq 4.8 \cdot 10^{-21}\right):\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+41} \lor \neg \left(y \leq 2.7 \cdot 10^{-44}\right):\\ \;\;\;\;y \cdot \left(z + y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.15e+41) (not (<= y 2.7e-44)))
   (* y (+ z (* y x)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e+41) || !(y <= 2.7e-44)) {
		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 <= (-1.15d+41)) .or. (.not. (y <= 2.7d-44))) 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 <= -1.15e+41) || !(y <= 2.7e-44)) {
		tmp = y * (z + (y * x));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.15e+41) or not (y <= 2.7e-44):
		tmp = y * (z + (y * x))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.15e+41) || !(y <= 2.7e-44))
		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 <= -1.15e+41) || ~((y <= 2.7e-44)))
		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, -1.15e+41], N[Not[LessEqual[y, 2.7e-44]], $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 < -1.1499999999999999e41 or 2.6999999999999999e-44 < y

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 94.6%

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

   if -1.1499999999999999e41 < y < 2.6999999999999999e-44

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.1%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+41} \lor \neg \left(y \leq 2.7 \cdot 10^{-44}\right):\\ \;\;\;\;y \cdot \left(z + y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+105} \lor \neg \left(y \leq 5 \cdot 10^{+124}\right):\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.8e+105) (not (<= y 5e+124))) (* y (* y x)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.8e+105) || !(y <= 5e+124)) {
		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 <= (-5.8d+105)) .or. (.not. (y <= 5d+124))) 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 <= -5.8e+105) || !(y <= 5e+124)) {
		tmp = y * (y * x);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.8e+105) or not (y <= 5e+124):
		tmp = y * (y * x)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.8e+105) || !(y <= 5e+124))
		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 <= -5.8e+105) || ~((y <= 5e+124)))
		tmp = y * (y * x);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.8e+105], N[Not[LessEqual[y, 5e+124]], $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 < -5.8000000000000002e105 or 4.9999999999999996e124 < y

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 98.6%

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

   6. Taylor expanded in z around 0 88.4%

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

      1. *-commutative 88.4%

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

   8. Simplified 88.4%

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

   if -5.8000000000000002e105 < y < 4.9999999999999996e124

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.7%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+105} \lor \neg \left(y \leq 5 \cdot 10^{+124}\right):\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+201} \lor \neg \left(z \leq 6.8 \cdot 10^{+159}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.8e+201) (not (<= z 6.8e+159))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+201) || !(z <= 6.8e+159)) {
		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 <= (-3.8d+201)) .or. (.not. (z <= 6.8d+159))) 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 <= -3.8e+201) || !(z <= 6.8e+159)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.8e+201) or not (z <= 6.8e+159):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.8e+201) || !(z <= 6.8e+159))
		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 <= -3.8e+201) || ~((z <= 6.8e+159)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.8e+201], N[Not[LessEqual[z, 6.8e+159]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -3.79999999999999995e201 or 6.79999999999999983e159 < z

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 84.3%

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

   6. Taylor expanded in z around inf 74.0%

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

   if -3.79999999999999995e201 < z < 6.79999999999999983e159

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 55.3%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+201} \lor \neg \left(z \leq 6.8 \cdot 10^{+159}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 100.0%

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

3. Final simplification 100.0%

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

Alternative 7: 38.5% 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. Step-by-step derivation

   1. fma-def 100.0%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 45.2%

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

6. Final simplification 45.2%

   \[\leadsto t \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024020 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))