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

Percentage Accurate: 100.0% → 100.0%

Time: 7.1s

Alternatives: 6

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 99.7%

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

   1. associate-+l- 99.7%

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

   2. *-commutative 99.7%

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

   3. associate-+l- 99.7%

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

   4. metadata-eval 99.7%

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

   5. *-commutative 99.7%

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

   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: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+84} \lor \neg \left(y \cdot z \leq 5 \cdot 10^{-43}\right):\\ \;\;\;\;t - y \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -5e+84) (not (<= (* y z) 5e-43)))
   (- t (* y (* z 0.5)))
   (+ (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -5e+84) || !((y * z) <= 5e-43)) {
		tmp = t - (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) <= (-5d+84)) .or. (.not. ((y * z) <= 5d-43))) then
        tmp = t - (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) <= -5e+84) || !((y * z) <= 5e-43)) {
		tmp = t - (y * (z * 0.5));
	} else {
		tmp = (0.125 * x) + t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y * z) <= -5e+84) or not ((y * z) <= 5e-43):
		tmp = t - (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) <= -5e+84) || !(Float64(y * z) <= 5e-43))
		tmp = Float64(t - 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 (((y * z) <= -5e+84) || ~(((y * z) <= 5e-43)))
		tmp = t - (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], -5e+84], N[Not[LessEqual[N[(y * z), $MachinePrecision], 5e-43]], $MachinePrecision]], N[(t - N[(y * N[(z * 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) < -5.0000000000000001e84 or 5.00000000000000019e-43 < (*.f64 y z)

   1. Initial program 99.3%

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

      1. associate-+l- 99.3%

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

      2. *-commutative 99.3%

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

      3. associate-+l- 99.3%

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

      4. metadata-eval 99.3%

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

      5. *-commutative 99.3%

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

      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 87.6%

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

      1. *-commutative 87.6%

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

      2. associate-*r* 88.3%

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

   7. Simplified 88.3%

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

   if -5.0000000000000001e84 < (*.f64 y z) < 5.00000000000000019e-43

   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 92.5%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+84} \lor \neg \left(y \cdot z \leq 5 \cdot 10^{-43}\right):\\ \;\;\;\;t - y \cdot \left(z \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1.8 \cdot 10^{+151} \lor \neg \left(y \cdot z \leq 5.6 \cdot 10^{-44}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -1.8e+151) (not (<= (* y z) 5.6e-44)))
   (* (* y z) -0.5)
   t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -1.8e+151) || !((y * z) <= 5.6e-44)) {
		tmp = (y * z) * -0.5;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((y * z) <= (-1.8d+151)) .or. (.not. ((y * z) <= 5.6d-44))) then
        tmp = (y * z) * (-0.5d0)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -1.8e+151) || !((y * z) <= 5.6e-44)) {
		tmp = (y * z) * -0.5;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y * z) <= -1.8e+151) or not ((y * z) <= 5.6e-44):
		tmp = (y * z) * -0.5
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y * z) <= -1.8e+151) || !(Float64(y * z) <= 5.6e-44))
		tmp = Float64(Float64(y * z) * -0.5);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y * z) <= -1.8e+151) || ~(((y * z) <= 5.6e-44)))
		tmp = (y * z) * -0.5;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -1.8e+151], N[Not[LessEqual[N[(y * z), $MachinePrecision], 5.6e-44]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * -0.5), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.8e151 or 5.6e-44 < (*.f64 y z)

   1. Initial program 99.2%

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

      1. associate-+l- 99.2%

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

      2. *-commutative 99.2%

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

      3. associate-+l- 99.2%

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

      4. metadata-eval 99.2%

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

      5. *-commutative 99.2%

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

      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 87.6%

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

      1. *-commutative 87.6%

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

      2. associate-*r* 88.3%

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

   7. Simplified 88.3%

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

      1. metadata-eval 88.3%

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

      2. div-inv 88.3%

         \[\leadsto t - y \cdot \color{blue}{\frac{z}{2}} \]

      3. clear-num 88.2%

         \[\leadsto t - y \cdot \color{blue}{\frac{1}{\frac{2}{z}}} \]

      4. div-inv 88.1%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{2}{z}}} \]

   9. Applied egg-rr 88.1%

      \[\leadsto t - \color{blue}{\frac{y}{\frac{2}{z}}} \]

   10. Taylor expanded in t around 0 69.9%

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

   if -1.8e151 < (*.f64 y z) < 5.6e-44

   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 42.4%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1.8 \cdot 10^{+151} \lor \neg \left(y \cdot z \leq 5.6 \cdot 10^{-44}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+159}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+95}:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* y z) -5e+159)
   (* (* y z) -0.5)
   (if (<= (* y z) 2e+95) (+ (* 0.125 x) t) (* y (* z -0.5)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y * z) <= -5e+159) {
		tmp = (y * z) * -0.5;
	} else if ((y * z) <= 2e+95) {
		tmp = (0.125 * x) + t;
	} else {
		tmp = 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 ((y * z) <= (-5d+159)) then
        tmp = (y * z) * (-0.5d0)
    else if ((y * z) <= 2d+95) then
        tmp = (0.125d0 * x) + t
    else
        tmp = 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 ((y * z) <= -5e+159) {
		tmp = (y * z) * -0.5;
	} else if ((y * z) <= 2e+95) {
		tmp = (0.125 * x) + t;
	} else {
		tmp = y * (z * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y * z) <= -5e+159:
		tmp = (y * z) * -0.5
	elif (y * z) <= 2e+95:
		tmp = (0.125 * x) + t
	else:
		tmp = y * (z * -0.5)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y * z) <= -5e+159)
		tmp = Float64(Float64(y * z) * -0.5);
	elseif (Float64(y * z) <= 2e+95)
		tmp = Float64(Float64(0.125 * x) + t);
	else
		tmp = Float64(y * Float64(z * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y * z) <= -5e+159)
		tmp = (y * z) * -0.5;
	elseif ((y * z) <= 2e+95)
		tmp = (0.125 * x) + t;
	else
		tmp = y * (z * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(y * z), $MachinePrecision], -5e+159], N[(N[(y * z), $MachinePrecision] * -0.5), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 2e+95], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision], N[(y * N[(z * -0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5.00000000000000003e159

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*r* 92.7%

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

   7. Simplified 92.7%

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

      1. metadata-eval 92.7%

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

      2. div-inv 92.7%

         \[\leadsto t - y \cdot \color{blue}{\frac{z}{2}} \]

      3. clear-num 92.6%

         \[\leadsto t - y \cdot \color{blue}{\frac{1}{\frac{2}{z}}} \]

      4. div-inv 92.5%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{2}{z}}} \]

   9. Applied egg-rr 92.5%

      \[\leadsto t - \color{blue}{\frac{y}{\frac{2}{z}}} \]

   10. Taylor expanded in t around 0 80.5%

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

   if -5.00000000000000003e159 < (*.f64 y z) < 2.00000000000000004e95

   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 85.9%

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

   if 2.00000000000000004e95 < (*.f64 y z)

   1. Initial program 98.2%

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

      1. associate-+l- 98.2%

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

      2. *-commutative 98.2%

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

      3. associate-+l- 98.2%

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

      4. metadata-eval 98.2%

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

      5. *-commutative 98.2%

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

      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 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-*r* 88.3%

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

   7. Simplified 88.3%

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

      1. metadata-eval 88.3%

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

      2. div-inv 88.3%

         \[\leadsto t - y \cdot \color{blue}{\frac{z}{2}} \]

      3. clear-num 88.2%

         \[\leadsto t - y \cdot \color{blue}{\frac{1}{\frac{2}{z}}} \]

      4. div-inv 88.1%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{2}{z}}} \]

   9. Applied egg-rr 88.1%

      \[\leadsto t - \color{blue}{\frac{y}{\frac{2}{z}}} \]

   10. Taylor expanded in t around 0 76.1%

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

       1. add-log-exp 49.4%

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

       2. *-un-lft-identity 49.4%

          \[\leadsto \log \color{blue}{\left(1 \cdot e^{-0.5 \cdot \left(y \cdot z\right)}\right)} \]

       3. log-prod 49.4%

          \[\leadsto \color{blue}{\log 1 + \log \left(e^{-0.5 \cdot \left(y \cdot z\right)}\right)} \]

       4. metadata-eval 49.4%

          \[\leadsto \color{blue}{0} + \log \left(e^{-0.5 \cdot \left(y \cdot z\right)}\right) \]

       5. add-log-exp 76.1%

          \[\leadsto 0 + \color{blue}{-0.5 \cdot \left(y \cdot z\right)} \]

       6. *-commutative 76.1%

          \[\leadsto 0 + \color{blue}{\left(y \cdot z\right) \cdot -0.5} \]

       7. associate-*l* 77.9%

          \[\leadsto 0 + \color{blue}{y \cdot \left(z \cdot -0.5\right)} \]

   12. Applied egg-rr 77.9%

       \[\leadsto \color{blue}{0 + y \cdot \left(z \cdot -0.5\right)} \]
   13. Step-by-step derivation

       1. +-lft-identity 77.9%

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

   14. Simplified 77.9%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+159}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+95}:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+159}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{elif}\;y \cdot z \leq 10^{-56}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* y z) -5e+159)
   (* (* y z) -0.5)
   (if (<= (* y z) 1e-56) t (* y (* z -0.5)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y * z) <= -5e+159) {
		tmp = (y * z) * -0.5;
	} else if ((y * z) <= 1e-56) {
		tmp = t;
	} else {
		tmp = 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 ((y * z) <= (-5d+159)) then
        tmp = (y * z) * (-0.5d0)
    else if ((y * z) <= 1d-56) then
        tmp = t
    else
        tmp = 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 ((y * z) <= -5e+159) {
		tmp = (y * z) * -0.5;
	} else if ((y * z) <= 1e-56) {
		tmp = t;
	} else {
		tmp = y * (z * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y * z) <= -5e+159:
		tmp = (y * z) * -0.5
	elif (y * z) <= 1e-56:
		tmp = t
	else:
		tmp = y * (z * -0.5)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y * z) <= -5e+159)
		tmp = Float64(Float64(y * z) * -0.5);
	elseif (Float64(y * z) <= 1e-56)
		tmp = t;
	else
		tmp = Float64(y * Float64(z * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y * z) <= -5e+159)
		tmp = (y * z) * -0.5;
	elseif ((y * z) <= 1e-56)
		tmp = t;
	else
		tmp = y * (z * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(y * z), $MachinePrecision], -5e+159], N[(N[(y * z), $MachinePrecision] * -0.5), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 1e-56], t, N[(y * N[(z * -0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5.00000000000000003e159

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-+l- 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*r* 92.7%

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

   7. Simplified 92.7%

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

      1. metadata-eval 92.7%

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

      2. div-inv 92.7%

         \[\leadsto t - y \cdot \color{blue}{\frac{z}{2}} \]

      3. clear-num 92.6%

         \[\leadsto t - y \cdot \color{blue}{\frac{1}{\frac{2}{z}}} \]

      4. div-inv 92.5%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{2}{z}}} \]

   9. Applied egg-rr 92.5%

      \[\leadsto t - \color{blue}{\frac{y}{\frac{2}{z}}} \]

   10. Taylor expanded in t around 0 80.5%

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

   if -5.00000000000000003e159 < (*.f64 y z) < 1e-56

   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 42.4%

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

   if 1e-56 < (*.f64 y z)

   1. Initial program 98.9%

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

      1. associate-+l- 98.9%

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

      2. *-commutative 98.9%

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

      3. associate-+l- 98.9%

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

      4. metadata-eval 98.9%

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

      5. *-commutative 98.9%

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

      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 84.7%

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

      1. *-commutative 84.7%

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

      2. associate-*r* 85.8%

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

   7. Simplified 85.8%

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

      1. metadata-eval 85.8%

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

      2. div-inv 85.8%

         \[\leadsto t - y \cdot \color{blue}{\frac{z}{2}} \]

      3. clear-num 85.7%

         \[\leadsto t - y \cdot \color{blue}{\frac{1}{\frac{2}{z}}} \]

      4. div-inv 85.6%

         \[\leadsto t - \color{blue}{\frac{y}{\frac{2}{z}}} \]

   9. Applied egg-rr 85.6%

      \[\leadsto t - \color{blue}{\frac{y}{\frac{2}{z}}} \]

   10. Taylor expanded in t around 0 63.9%

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

       1. add-log-exp 34.2%

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

       2. *-un-lft-identity 34.2%

          \[\leadsto \log \color{blue}{\left(1 \cdot e^{-0.5 \cdot \left(y \cdot z\right)}\right)} \]

       3. log-prod 34.2%

          \[\leadsto \color{blue}{\log 1 + \log \left(e^{-0.5 \cdot \left(y \cdot z\right)}\right)} \]

       4. metadata-eval 34.2%

          \[\leadsto \color{blue}{0} + \log \left(e^{-0.5 \cdot \left(y \cdot z\right)}\right) \]

       5. add-log-exp 63.9%

          \[\leadsto 0 + \color{blue}{-0.5 \cdot \left(y \cdot z\right)} \]

       6. *-commutative 63.9%

          \[\leadsto 0 + \color{blue}{\left(y \cdot z\right) \cdot -0.5} \]

       7. associate-*l* 65.1%

          \[\leadsto 0 + \color{blue}{y \cdot \left(z \cdot -0.5\right)} \]

   12. Applied egg-rr 65.1%

       \[\leadsto \color{blue}{0 + y \cdot \left(z \cdot -0.5\right)} \]
   13. Step-by-step derivation

       1. +-lft-identity 65.1%

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

   14. Simplified 65.1%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+159}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{elif}\;y \cdot z \leq 10^{-56}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 32.9% 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 99.7%

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

   1. associate-+l- 99.7%

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

   2. *-commutative 99.7%

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

   3. associate-+l- 99.7%

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

   4. metadata-eval 99.7%

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

   5. *-commutative 99.7%

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

   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 32.6%

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

Developer Target 1: 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 2024137 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (- (+ (/ x 8) t) (* (/ z 2) y)))

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