Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, B

Percentage Accurate: 100.0% → 100.0%

Time: 6.8s

Alternatives: 7

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + 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 = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Python

def code(x, y, z, t):
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + 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 = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Python

def code(x, y, z, t):
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ (- (* 0.125 x) (* y (/ z 2.0))) t))

C

double code(double x, double y, double z, double t) {
	return ((0.125 * x) - (y * (z / 2.0))) + 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 = ((0.125d0 * x) - (y * (z / 2.0d0))) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((0.125 * x) - (y * (z / 2.0))) + t;
}

Python

def code(x, y, z, t):
	return ((0.125 * x) - (y * (z / 2.0))) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(0.125 * x) - Float64(y * Float64(z / 2.0))) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((0.125 * x) - (y * (z / 2.0))) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(0.125 * x), $MachinePrecision] - N[(y * N[(z / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Step-by-step derivation

   1. associate-+l- 100.0%

      \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

   2. *-commutative 100.0%

      \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

   3. associate-+l- 100.0%

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

   4. metadata-eval 100.0%

      \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

   5. *-commutative 100.0%

      \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

   6. associate-/l* 100.0%

      \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 86.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - y \cdot \left(z \cdot 0.5\right)\\ \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{-68}:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{elif}\;y \cdot z \leq 10^{-14} \lor \neg \left(y \cdot z \leq 10^{+99}\right):\\ \;\;\;\;0.125 \cdot x + \left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- t (* y (* z 0.5)))))
   (if (<= (* y z) -1e+141)
     t_1
     (if (<= (* y z) 5e-68)
       (+ (* 0.125 x) t)
       (if (or (<= (* y z) 1e-14) (not (<= (* y z) 1e+99)))
         (+ (* 0.125 x) (* (* y z) -0.5))
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t - (y * (z * 0.5));
	double tmp;
	if ((y * z) <= -1e+141) {
		tmp = t_1;
	} else if ((y * z) <= 5e-68) {
		tmp = (0.125 * x) + t;
	} else if (((y * z) <= 1e-14) || !((y * z) <= 1e+99)) {
		tmp = (0.125 * x) + ((y * z) * -0.5);
	} 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 * 0.5d0))
    if ((y * z) <= (-1d+141)) then
        tmp = t_1
    else if ((y * z) <= 5d-68) then
        tmp = (0.125d0 * x) + t
    else if (((y * z) <= 1d-14) .or. (.not. ((y * z) <= 1d+99))) then
        tmp = (0.125d0 * x) + ((y * z) * (-0.5d0))
    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 * 0.5));
	double tmp;
	if ((y * z) <= -1e+141) {
		tmp = t_1;
	} else if ((y * z) <= 5e-68) {
		tmp = (0.125 * x) + t;
	} else if (((y * z) <= 1e-14) || !((y * z) <= 1e+99)) {
		tmp = (0.125 * x) + ((y * z) * -0.5);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t - (y * (z * 0.5))
	tmp = 0
	if (y * z) <= -1e+141:
		tmp = t_1
	elif (y * z) <= 5e-68:
		tmp = (0.125 * x) + t
	elif ((y * z) <= 1e-14) or not ((y * z) <= 1e+99):
		tmp = (0.125 * x) + ((y * z) * -0.5)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t - Float64(y * Float64(z * 0.5)))
	tmp = 0.0
	if (Float64(y * z) <= -1e+141)
		tmp = t_1;
	elseif (Float64(y * z) <= 5e-68)
		tmp = Float64(Float64(0.125 * x) + t);
	elseif ((Float64(y * z) <= 1e-14) || !(Float64(y * z) <= 1e+99))
		tmp = Float64(Float64(0.125 * x) + Float64(Float64(y * z) * -0.5));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t - (y * (z * 0.5));
	tmp = 0.0;
	if ((y * z) <= -1e+141)
		tmp = t_1;
	elseif ((y * z) <= 5e-68)
		tmp = (0.125 * x) + t;
	elseif (((y * z) <= 1e-14) || ~(((y * z) <= 1e+99)))
		tmp = (0.125 * x) + ((y * z) * -0.5);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t - N[(y * N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -1e+141], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], 5e-68], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision], If[Or[LessEqual[N[(y * z), $MachinePrecision], 1e-14], N[Not[LessEqual[N[(y * z), $MachinePrecision], 1e+99]], $MachinePrecision]], N[(N[(0.125 * x), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -1.00000000000000002e141 or 9.99999999999999999e-15 < (*.f64 y z) < 9.9999999999999997e98

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 92.3%

      \[\leadsto \color{blue}{t - 0.5 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 92.3%

         \[\leadsto t - \color{blue}{\left(y \cdot z\right) \cdot 0.5} \]

      2. associate-*r* 92.3%

         \[\leadsto t - \color{blue}{y \cdot \left(z \cdot 0.5\right)} \]

   7. Simplified 92.3%

      \[\leadsto \color{blue}{t - y \cdot \left(z \cdot 0.5\right)} \]

   if -1.00000000000000002e141 < (*.f64 y z) < 4.99999999999999971e-68

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 93.0%

      \[\leadsto \color{blue}{0.125 \cdot x} + t \]

   if 4.99999999999999971e-68 < (*.f64 y z) < 9.99999999999999999e-15 or 9.9999999999999997e98 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 93.8%

      \[\leadsto \color{blue}{y \cdot \left(0.125 \cdot \frac{x}{y} - 0.5 \cdot z\right)} + t \]

   6. Taylor expanded in t around 0 89.1%

      \[\leadsto \color{blue}{y \cdot \left(0.125 \cdot \frac{x}{y} - 0.5 \cdot z\right)} \]

   7. Taylor expanded in y around 0 95.4%

      \[\leadsto \color{blue}{-0.5 \cdot \left(y \cdot z\right) + 0.125 \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+141}:\\ \;\;\;\;t - y \cdot \left(z \cdot 0.5\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{-68}:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{elif}\;y \cdot z \leq 10^{-14} \lor \neg \left(y \cdot z \leq 10^{+99}\right):\\ \;\;\;\;0.125 \cdot x + \left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \left(z \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z \cdot -0.5\right)\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+54}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-260}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-24}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* z -0.5))))
   (if (<= x -3.1e+54)
     (* 0.125 x)
     (if (<= x -3e-260)
       t
       (if (<= x 1.52e-65)
         t_1
         (if (<= x 7.8e-24) t (if (<= x 5.4e+35) t_1 (* 0.125 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z * -0.5);
	double tmp;
	if (x <= -3.1e+54) {
		tmp = 0.125 * x;
	} else if (x <= -3e-260) {
		tmp = t;
	} else if (x <= 1.52e-65) {
		tmp = t_1;
	} else if (x <= 7.8e-24) {
		tmp = t;
	} else if (x <= 5.4e+35) {
		tmp = t_1;
	} else {
		tmp = 0.125 * x;
	}
	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 * (-0.5d0))
    if (x <= (-3.1d+54)) then
        tmp = 0.125d0 * x
    else if (x <= (-3d-260)) then
        tmp = t
    else if (x <= 1.52d-65) then
        tmp = t_1
    else if (x <= 7.8d-24) then
        tmp = t
    else if (x <= 5.4d+35) then
        tmp = t_1
    else
        tmp = 0.125d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z * -0.5);
	double tmp;
	if (x <= -3.1e+54) {
		tmp = 0.125 * x;
	} else if (x <= -3e-260) {
		tmp = t;
	} else if (x <= 1.52e-65) {
		tmp = t_1;
	} else if (x <= 7.8e-24) {
		tmp = t;
	} else if (x <= 5.4e+35) {
		tmp = t_1;
	} else {
		tmp = 0.125 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z * -0.5)
	tmp = 0
	if x <= -3.1e+54:
		tmp = 0.125 * x
	elif x <= -3e-260:
		tmp = t
	elif x <= 1.52e-65:
		tmp = t_1
	elif x <= 7.8e-24:
		tmp = t
	elif x <= 5.4e+35:
		tmp = t_1
	else:
		tmp = 0.125 * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z * -0.5))
	tmp = 0.0
	if (x <= -3.1e+54)
		tmp = Float64(0.125 * x);
	elseif (x <= -3e-260)
		tmp = t;
	elseif (x <= 1.52e-65)
		tmp = t_1;
	elseif (x <= 7.8e-24)
		tmp = t;
	elseif (x <= 5.4e+35)
		tmp = t_1;
	else
		tmp = Float64(0.125 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z * -0.5);
	tmp = 0.0;
	if (x <= -3.1e+54)
		tmp = 0.125 * x;
	elseif (x <= -3e-260)
		tmp = t;
	elseif (x <= 1.52e-65)
		tmp = t_1;
	elseif (x <= 7.8e-24)
		tmp = t;
	elseif (x <= 5.4e+35)
		tmp = t_1;
	else
		tmp = 0.125 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z * -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.1e+54], N[(0.125 * x), $MachinePrecision], If[LessEqual[x, -3e-260], t, If[LessEqual[x, 1.52e-65], t$95$1, If[LessEqual[x, 7.8e-24], t, If[LessEqual[x, 5.4e+35], t$95$1, N[(0.125 * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.0999999999999999e54 or 5.40000000000000005e35 < x

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.4%

      \[\leadsto \color{blue}{y \cdot \left(0.125 \cdot \frac{x}{y} - 0.5 \cdot z\right)} + t \]

   6. Taylor expanded in t around 0 54.0%

      \[\leadsto \color{blue}{y \cdot \left(0.125 \cdot \frac{x}{y} - 0.5 \cdot z\right)} \]

   7. Taylor expanded in y around 0 64.1%

      \[\leadsto \color{blue}{0.125 \cdot x} \]

   if -3.0999999999999999e54 < x < -3.0000000000000001e-260 or 1.5199999999999999e-65 < x < 7.8e-24

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 57.8%

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

   if -3.0000000000000001e-260 < x < 1.5199999999999999e-65 or 7.8e-24 < x < 5.40000000000000005e35

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{y \cdot \left(0.125 \cdot \frac{x}{y} - 0.5 \cdot z\right)} + t \]

   6. Taylor expanded in t around 0 70.9%

      \[\leadsto \color{blue}{y \cdot \left(0.125 \cdot \frac{x}{y} - 0.5 \cdot z\right)} \]

   7. Taylor expanded in y around inf 60.9%

      \[\leadsto \color{blue}{-0.5 \cdot \left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 60.9%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot -0.5} \]

      2. associate-*l* 60.9%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot -0.5\right)} \]

      3. *-commutative 60.9%

         \[\leadsto y \cdot \color{blue}{\left(-0.5 \cdot z\right)} \]

   9. Simplified 60.9%

      \[\leadsto \color{blue}{y \cdot \left(-0.5 \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+54}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-260}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-24}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+117} \lor \neg \left(x \leq 1.85 \cdot 10^{+35}\right):\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \left(z \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.2e+117) (not (<= x 1.85e+35)))
   (+ (* 0.125 x) t)
   (- t (* y (* z 0.5)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.2e+117) || !(x <= 1.85e+35)) {
		tmp = (0.125 * x) + t;
	} else {
		tmp = t - (y * (z * 0.5));
	}
	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 ((x <= (-4.2d+117)) .or. (.not. (x <= 1.85d+35))) then
        tmp = (0.125d0 * x) + t
    else
        tmp = t - (y * (z * 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.2e+117) || !(x <= 1.85e+35)) {
		tmp = (0.125 * x) + t;
	} else {
		tmp = t - (y * (z * 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.2e+117) or not (x <= 1.85e+35):
		tmp = (0.125 * x) + t
	else:
		tmp = t - (y * (z * 0.5))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.2e+117) || !(x <= 1.85e+35))
		tmp = Float64(Float64(0.125 * x) + t);
	else
		tmp = Float64(t - Float64(y * Float64(z * 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.2e+117) || ~((x <= 1.85e+35)))
		tmp = (0.125 * x) + t;
	else
		tmp = t - (y * (z * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.2e+117], N[Not[LessEqual[x, 1.85e+35]], $MachinePrecision]], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision], N[(t - N[(y * N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2000000000000002e117 or 1.85e35 < x

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 82.9%

      \[\leadsto \color{blue}{0.125 \cdot x} + t \]

   if -4.2000000000000002e117 < x < 1.85e35

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 87.9%

      \[\leadsto \color{blue}{t - 0.5 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 87.9%

         \[\leadsto t - \color{blue}{\left(y \cdot z\right) \cdot 0.5} \]

      2. associate-*r* 87.9%

         \[\leadsto t - \color{blue}{y \cdot \left(z \cdot 0.5\right)} \]

   7. Simplified 87.9%

      \[\leadsto \color{blue}{t - y \cdot \left(z \cdot 0.5\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+117} \lor \neg \left(x \leq 1.85 \cdot 10^{+35}\right):\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t - y \cdot \left(z \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-6} \lor \neg \left(z \leq 8.8 \cdot 10^{+167}\right):\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.4e-6) (not (<= z 8.8e+167)))
   (* y (* z -0.5))
   (+ (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.4e-6) || !(z <= 8.8e+167)) {
		tmp = y * (z * -0.5);
	} else {
		tmp = (0.125 * x) + 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 <= (-5.4d-6)) .or. (.not. (z <= 8.8d+167))) then
        tmp = y * (z * (-0.5d0))
    else
        tmp = (0.125d0 * x) + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.4e-6) || !(z <= 8.8e+167)) {
		tmp = y * (z * -0.5);
	} else {
		tmp = (0.125 * x) + t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.4e-6) or not (z <= 8.8e+167):
		tmp = y * (z * -0.5)
	else:
		tmp = (0.125 * x) + t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.4e-6) || !(z <= 8.8e+167))
		tmp = Float64(y * Float64(z * -0.5));
	else
		tmp = Float64(Float64(0.125 * x) + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.4e-6) || ~((z <= 8.8e+167)))
		tmp = y * (z * -0.5);
	else
		tmp = (0.125 * x) + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.4e-6], N[Not[LessEqual[z, 8.8e+167]], $MachinePrecision]], N[(y * N[(z * -0.5), $MachinePrecision]), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.39999999999999997e-6 or 8.80000000000000013e167 < z

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 87.7%

      \[\leadsto \color{blue}{y \cdot \left(0.125 \cdot \frac{x}{y} - 0.5 \cdot z\right)} + t \]

   6. Taylor expanded in t around 0 66.2%

      \[\leadsto \color{blue}{y \cdot \left(0.125 \cdot \frac{x}{y} - 0.5 \cdot z\right)} \]

   7. Taylor expanded in y around inf 60.0%

      \[\leadsto \color{blue}{-0.5 \cdot \left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 60.0%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot -0.5} \]

      2. associate-*l* 60.0%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot -0.5\right)} \]

      3. *-commutative 60.0%

         \[\leadsto y \cdot \color{blue}{\left(-0.5 \cdot z\right)} \]

   9. Simplified 60.0%

      \[\leadsto \color{blue}{y \cdot \left(-0.5 \cdot z\right)} \]

   if -5.39999999999999997e-6 < z < 8.80000000000000013e167

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 78.6%

      \[\leadsto \color{blue}{0.125 \cdot x} + t \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-6} \lor \neg \left(z \leq 8.8 \cdot 10^{+167}\right):\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+55} \lor \neg \left(x \leq 2900000000000\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.4e+55) (not (<= x 2900000000000.0))) (* 0.125 x) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.4e+55) || !(x <= 2900000000000.0)) {
		tmp = 0.125 * 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 ((x <= (-5.4d+55)) .or. (.not. (x <= 2900000000000.0d0))) then
        tmp = 0.125d0 * 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 ((x <= -5.4e+55) || !(x <= 2900000000000.0)) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.4e+55) or not (x <= 2900000000000.0):
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.4e+55) || !(x <= 2900000000000.0))
		tmp = Float64(0.125 * x);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.4e+55) || ~((x <= 2900000000000.0)))
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.4e+55], N[Not[LessEqual[x, 2900000000000.0]], $MachinePrecision]], N[(0.125 * x), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -5.39999999999999954e55 or 2.9e12 < x

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 65.7%

      \[\leadsto \color{blue}{y \cdot \left(0.125 \cdot \frac{x}{y} - 0.5 \cdot z\right)} + t \]

   6. Taylor expanded in t around 0 55.8%

      \[\leadsto \color{blue}{y \cdot \left(0.125 \cdot \frac{x}{y} - 0.5 \cdot z\right)} \]

   7. Taylor expanded in y around 0 62.7%

      \[\leadsto \color{blue}{0.125 \cdot x} \]

   if -5.39999999999999954e55 < x < 2.9e12

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

      3. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

      4. metadata-eval 100.0%

         \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

      5. *-commutative 100.0%

         \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

      6. associate-/l* 100.0%

         \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 45.0%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+55} \lor \neg \left(x \leq 2900000000000\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 32.8% accurate, 13.0× 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%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Step-by-step derivation

   1. associate-+l- 100.0%

      \[\leadsto \color{blue}{\frac{1}{8} \cdot x - \left(\frac{y \cdot z}{2} - t\right)} \]

   2. *-commutative 100.0%

      \[\leadsto \frac{1}{8} \cdot x - \left(\frac{\color{blue}{z \cdot y}}{2} - t\right) \]

   3. associate-+l- 100.0%

      \[\leadsto \color{blue}{\left(\frac{1}{8} \cdot x - \frac{z \cdot y}{2}\right) + t} \]

   4. metadata-eval 100.0%

      \[\leadsto \left(\color{blue}{0.125} \cdot x - \frac{z \cdot y}{2}\right) + t \]

   5. *-commutative 100.0%

      \[\leadsto \left(0.125 \cdot x - \frac{\color{blue}{y \cdot z}}{2}\right) + t \]

   6. associate-/l* 100.0%

      \[\leadsto \left(0.125 \cdot x - \color{blue}{y \cdot \frac{z}{2}}\right) + t \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\left(0.125 \cdot x - y \cdot \frac{z}{2}\right) + t} \]
4. Add Preprocessing

5. Taylor expanded in t around inf 33.2%

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

Developer target: 100.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \left(\frac{x}{8} + t\right) - \frac{z}{2} \cdot y \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (+ (/ x 8.0) t) (* (/ z 2.0) y)))

C

double code(double x, double y, double z, double t) {
	return ((x / 8.0) + t) - ((z / 2.0) * 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 = ((x / 8.0d0) + t) - ((z / 2.0d0) * y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x / 8.0) + t) - ((z / 2.0) * y);
}

Python

def code(x, y, z, t):
	return ((x / 8.0) + t) - ((z / 2.0) * y)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x / 8.0) + t) - Float64(Float64(z / 2.0) * y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x / 8.0) + t) - ((z / 2.0) * y);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x / 8.0), $MachinePrecision] + t), $MachinePrecision] - N[(N[(z / 2.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024084 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (- (+ (/ x 8.0) t) (* (/ z 2.0) y))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))