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

Percentage Accurate: 99.9% → 99.9%

Time: 6.8s

Alternatives: 8

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: 99.9% 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: 99.9% accurate, 1.2× speedup

Math

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

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(Float64(y * 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[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 2: 50.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot z\right) \cdot -0.5\\ \mathbf{if}\;t \leq -3.25 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+34}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-126}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.185:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* y z) -0.5)))
   (if (<= t -3.25e+136)
     t
     (if (<= t -8.5e+43)
       t_1
       (if (<= t -6.5e+34)
         t
         (if (<= t -4.2e-126)
           (* 0.125 x)
           (if (<= t -5e-304) t_1 (if (<= t 0.185) (* 0.125 x) t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) * -0.5;
	double tmp;
	if (t <= -3.25e+136) {
		tmp = t;
	} else if (t <= -8.5e+43) {
		tmp = t_1;
	} else if (t <= -6.5e+34) {
		tmp = t;
	} else if (t <= -4.2e-126) {
		tmp = 0.125 * x;
	} else if (t <= -5e-304) {
		tmp = t_1;
	} else if (t <= 0.185) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (y * z) * (-0.5d0)
    if (t <= (-3.25d+136)) then
        tmp = t
    else if (t <= (-8.5d+43)) then
        tmp = t_1
    else if (t <= (-6.5d+34)) then
        tmp = t
    else if (t <= (-4.2d-126)) then
        tmp = 0.125d0 * x
    else if (t <= (-5d-304)) then
        tmp = t_1
    else if (t <= 0.185d0) 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 t_1 = (y * z) * -0.5;
	double tmp;
	if (t <= -3.25e+136) {
		tmp = t;
	} else if (t <= -8.5e+43) {
		tmp = t_1;
	} else if (t <= -6.5e+34) {
		tmp = t;
	} else if (t <= -4.2e-126) {
		tmp = 0.125 * x;
	} else if (t <= -5e-304) {
		tmp = t_1;
	} else if (t <= 0.185) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) * -0.5
	tmp = 0
	if t <= -3.25e+136:
		tmp = t
	elif t <= -8.5e+43:
		tmp = t_1
	elif t <= -6.5e+34:
		tmp = t
	elif t <= -4.2e-126:
		tmp = 0.125 * x
	elif t <= -5e-304:
		tmp = t_1
	elif t <= 0.185:
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) * -0.5)
	tmp = 0.0
	if (t <= -3.25e+136)
		tmp = t;
	elseif (t <= -8.5e+43)
		tmp = t_1;
	elseif (t <= -6.5e+34)
		tmp = t;
	elseif (t <= -4.2e-126)
		tmp = Float64(0.125 * x);
	elseif (t <= -5e-304)
		tmp = t_1;
	elseif (t <= 0.185)
		tmp = Float64(0.125 * x);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) * -0.5;
	tmp = 0.0;
	if (t <= -3.25e+136)
		tmp = t;
	elseif (t <= -8.5e+43)
		tmp = t_1;
	elseif (t <= -6.5e+34)
		tmp = t;
	elseif (t <= -4.2e-126)
		tmp = 0.125 * x;
	elseif (t <= -5e-304)
		tmp = t_1;
	elseif (t <= 0.185)
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] * -0.5), $MachinePrecision]}, If[LessEqual[t, -3.25e+136], t, If[LessEqual[t, -8.5e+43], t$95$1, If[LessEqual[t, -6.5e+34], t, If[LessEqual[t, -4.2e-126], N[(0.125 * x), $MachinePrecision], If[LessEqual[t, -5e-304], t$95$1, If[LessEqual[t, 0.185], N[(0.125 * x), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2499999999999999e136 or -8.5e43 < t < -6.50000000000000017e34 or 0.185 < t

   1. Initial program 100.0%

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

      1. add0 100.0%

         \[\leadsto \color{blue}{\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + 0\right)} + t \]

      2. add0 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 71.2%

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

   if -3.2499999999999999e136 < t < -8.5e43 or -4.1999999999999997e-126 < t < -4.99999999999999965e-304

   1. Initial program 100.0%

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

      1. add0 100.0%

         \[\leadsto \color{blue}{\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + 0\right)} + t \]

      2. add0 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-*r* 74.4%

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

      3. *-commutative 74.4%

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

      4. associate-*l* 74.4%

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

   7. Simplified 74.4%

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

   8. Taylor expanded in t around 0 66.2%

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

   if -6.50000000000000017e34 < t < -4.1999999999999997e-126 or -4.99999999999999965e-304 < t < 0.185

   1. Initial program 100.0%

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

      1. add0 100.0%

         \[\leadsto \color{blue}{\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + 0\right)} + t \]

      2. add0 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 91.6%

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

   6. Taylor expanded in x around inf 63.8%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.25 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+43}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+34}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-126}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-304}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{elif}\;t \leq 0.185:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot \left(y \cdot 0.5\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-71}:\\ \;\;\;\;0.125 \cdot x - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+106} \lor \neg \left(t \leq 1.2 \cdot 10^{+213}\right):\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- t (* z (* y 0.5)))))
   (if (<= t -1e+74)
     t_1
     (if (<= t 1.7e-71)
       (- (* 0.125 x) (* (* y z) 0.5))
       (if (or (<= t 5.4e+106) (not (<= t 1.2e+213)))
         (+ (* 0.125 x) t)
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t - (z * (y * 0.5));
	double tmp;
	if (t <= -1e+74) {
		tmp = t_1;
	} else if (t <= 1.7e-71) {
		tmp = (0.125 * x) - ((y * z) * 0.5);
	} else if ((t <= 5.4e+106) || !(t <= 1.2e+213)) {
		tmp = (0.125 * x) + t;
	} 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 - (z * (y * 0.5d0))
    if (t <= (-1d+74)) then
        tmp = t_1
    else if (t <= 1.7d-71) then
        tmp = (0.125d0 * x) - ((y * z) * 0.5d0)
    else if ((t <= 5.4d+106) .or. (.not. (t <= 1.2d+213))) then
        tmp = (0.125d0 * x) + t
    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 - (z * (y * 0.5));
	double tmp;
	if (t <= -1e+74) {
		tmp = t_1;
	} else if (t <= 1.7e-71) {
		tmp = (0.125 * x) - ((y * z) * 0.5);
	} else if ((t <= 5.4e+106) || !(t <= 1.2e+213)) {
		tmp = (0.125 * x) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t - (z * (y * 0.5))
	tmp = 0
	if t <= -1e+74:
		tmp = t_1
	elif t <= 1.7e-71:
		tmp = (0.125 * x) - ((y * z) * 0.5)
	elif (t <= 5.4e+106) or not (t <= 1.2e+213):
		tmp = (0.125 * x) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t - Float64(z * Float64(y * 0.5)))
	tmp = 0.0
	if (t <= -1e+74)
		tmp = t_1;
	elseif (t <= 1.7e-71)
		tmp = Float64(Float64(0.125 * x) - Float64(Float64(y * z) * 0.5));
	elseif ((t <= 5.4e+106) || !(t <= 1.2e+213))
		tmp = Float64(Float64(0.125 * x) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t - (z * (y * 0.5));
	tmp = 0.0;
	if (t <= -1e+74)
		tmp = t_1;
	elseif (t <= 1.7e-71)
		tmp = (0.125 * x) - ((y * z) * 0.5);
	elseif ((t <= 5.4e+106) || ~((t <= 1.2e+213)))
		tmp = (0.125 * x) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t - N[(z * N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+74], t$95$1, If[LessEqual[t, 1.7e-71], N[(N[(0.125 * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 5.4e+106], N[Not[LessEqual[t, 1.2e+213]], $MachinePrecision]], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.99999999999999952e73 or 5.40000000000000012e106 < t < 1.2e213

   1. Initial program 100.0%

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

      1. add0 100.0%

         \[\leadsto \color{blue}{\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + 0\right)} + t \]

      2. add0 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 93.3%

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

      1. *-commutative 93.3%

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

      2. associate-*r* 93.3%

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

      3. *-commutative 93.3%

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

      4. associate-*l* 93.3%

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

   7. Simplified 93.3%

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

   if -9.99999999999999952e73 < t < 1.70000000000000002e-71

   1. Initial program 100.0%

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

      1. add0 100.0%

         \[\leadsto \color{blue}{\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + 0\right)} + t \]

      2. add0 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 93.6%

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

   if 1.70000000000000002e-71 < t < 5.40000000000000012e106 or 1.2e213 < t

   1. Initial program 100.0%

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

      1. add0 100.0%

         \[\leadsto \color{blue}{\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + 0\right)} + t \]

      2. add0 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 91.8%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+74}:\\ \;\;\;\;t - z \cdot \left(y \cdot 0.5\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-71}:\\ \;\;\;\;0.125 \cdot x - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+106} \lor \neg \left(t \leq 1.2 \cdot 10^{+213}\right):\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t - z \cdot \left(y \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+36} \lor \neg \left(y \cdot z \leq 5 \cdot 10^{+164}\right):\\ \;\;\;\;t - z \cdot \left(y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -1e+36) (not (<= (* y z) 5e+164)))
   (- t (* z (* y 0.5)))
   (+ (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -1e+36) || !((y * z) <= 5e+164)) {
		tmp = t - (z * (y * 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 (((y * z) <= (-1d+36)) .or. (.not. ((y * z) <= 5d+164))) then
        tmp = t - (z * (y * 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 (((y * z) <= -1e+36) || !((y * z) <= 5e+164)) {
		tmp = t - (z * (y * 0.5));
	} else {
		tmp = (0.125 * x) + t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y * z) <= -1e+36) or not ((y * z) <= 5e+164):
		tmp = t - (z * (y * 0.5))
	else:
		tmp = (0.125 * x) + t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y * z) <= -1e+36) || !(Float64(y * z) <= 5e+164))
		tmp = Float64(t - Float64(z * Float64(y * 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 (((y * z) <= -1e+36) || ~(((y * z) <= 5e+164)))
		tmp = t - (z * (y * 0.5));
	else
		tmp = (0.125 * x) + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -1e+36], N[Not[LessEqual[N[(y * z), $MachinePrecision], 5e+164]], $MachinePrecision]], N[(t - N[(z * N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.00000000000000004e36 or 4.9999999999999995e164 < (*.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. add0 100.0%

         \[\leadsto \color{blue}{\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + 0\right)} + t \]

      2. add0 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*r* 90.6%

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

      3. *-commutative 90.6%

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

      4. associate-*l* 90.6%

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

   7. Simplified 90.6%

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

   if -1.00000000000000004e36 < (*.f64 y z) < 4.9999999999999995e164

   1. Initial program 100.0%

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

      1. add0 100.0%

         \[\leadsto \color{blue}{\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + 0\right)} + t \]

      2. add0 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 88.9%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+36} \lor \neg \left(y \cdot z \leq 5 \cdot 10^{+164}\right):\\ \;\;\;\;t - z \cdot \left(y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1.05 \cdot 10^{+135} \lor \neg \left(y \cdot z \leq 2.9 \cdot 10^{+166}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -1.05e+135) (not (<= (* y z) 2.9e+166)))
   (* (* y z) -0.5)
   (+ (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -1.05e+135) || !((y * z) <= 2.9e+166)) {
		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 (((y * z) <= (-1.05d+135)) .or. (.not. ((y * z) <= 2.9d+166))) 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 (((y * z) <= -1.05e+135) || !((y * z) <= 2.9e+166)) {
		tmp = (y * z) * -0.5;
	} else {
		tmp = (0.125 * x) + t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y * z) <= -1.05e+135) or not ((y * z) <= 2.9e+166):
		tmp = (y * z) * -0.5
	else:
		tmp = (0.125 * x) + t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y * z) <= -1.05e+135) || !(Float64(y * z) <= 2.9e+166))
		tmp = Float64(Float64(y * 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 (((y * z) <= -1.05e+135) || ~(((y * z) <= 2.9e+166)))
		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[N[(y * z), $MachinePrecision], -1.05e+135], N[Not[LessEqual[N[(y * z), $MachinePrecision], 2.9e+166]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * -0.5), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.05000000000000005e135 or 2.9000000000000001e166 < (*.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. add0 100.0%

         \[\leadsto \color{blue}{\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + 0\right)} + t \]

      2. add0 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*r* 94.9%

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

      3. *-commutative 94.9%

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

      4. associate-*l* 94.9%

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

   7. Simplified 94.9%

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

   8. Taylor expanded in t around 0 88.9%

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

   if -1.05000000000000005e135 < (*.f64 y z) < 2.9000000000000001e166

   1. Initial program 100.0%

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

      1. add0 100.0%

         \[\leadsto \color{blue}{\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + 0\right)} + t \]

      2. add0 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 86.4%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1.05 \cdot 10^{+135} \lor \neg \left(y \cdot z \leq 2.9 \cdot 10^{+166}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 0.255:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.6e+72) t (if (<= t 0.255) (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.6e+72) {
		tmp = t;
	} else if (t <= 0.255) {
		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 (t <= (-5.6d+72)) then
        tmp = t
    else if (t <= 0.255d0) 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 (t <= -5.6e+72) {
		tmp = t;
	} else if (t <= 0.255) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.6e+72:
		tmp = t
	elif t <= 0.255:
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.6e+72)
		tmp = t;
	elseif (t <= 0.255)
		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 (t <= -5.6e+72)
		tmp = t;
	elseif (t <= 0.255)
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.6e+72], t, If[LessEqual[t, 0.255], N[(0.125 * x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5999999999999998e72 or 0.255 < t

   1. Initial program 100.0%

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

      1. add0 100.0%

         \[\leadsto \color{blue}{\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + 0\right)} + t \]

      2. add0 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 67.9%

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

   if -5.5999999999999998e72 < t < 0.255

   1. Initial program 100.0%

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

      1. add0 100.0%

         \[\leadsto \color{blue}{\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + 0\right)} + t \]

      2. add0 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 92.1%

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

   6. Taylor expanded in x around inf 51.1%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 0.255:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 + ((0.125d0 * x) - (y / (2.0d0 / z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(t + N[(N[(0.125 * x), $MachinePrecision] - N[(y / N[(2.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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. add0 100.0%

      \[\leadsto \color{blue}{\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + 0\right)} + t \]

   2. add0 100.0%

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

   3. metadata-eval 100.0%

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

   4. associate-/l* 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 8: 32.6% 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. add0 100.0%

      \[\leadsto \color{blue}{\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + 0\right)} + t \]

   2. add0 100.0%

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

   3. metadata-eval 100.0%

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

   4. associate-/l* 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in t around inf 35.7%

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

6. Final simplification 35.7%

   \[\leadsto t \]
7. 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 2024034 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

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

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