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

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

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: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -400000 \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+70}\right):\\ \;\;\;\;t - z \cdot \left(y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -400000.0) (not (<= (* y z) 2e+70)))
   (- 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) <= -400000.0) || !((y * z) <= 2e+70)) {
		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) <= (-400000.0d0)) .or. (.not. ((y * z) <= 2d+70))) 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) <= -400000.0) || !((y * z) <= 2e+70)) {
		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) <= -400000.0) or not ((y * z) <= 2e+70):
		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) <= -400000.0) || !(Float64(y * z) <= 2e+70))
		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) <= -400000.0) || ~(((y * z) <= 2e+70)))
		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], -400000.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 2e+70]], $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) < -4e5 or 2.00000000000000015e70 < (*.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 88.0%

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

      1. associate-*r* 88.7%

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

   7. Simplified 88.7%

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

   if -4e5 < (*.f64 y z) < 2.00000000000000015e70

   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 0 89.5%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -400000 \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+70}\right):\\ \;\;\;\;t - z \cdot \left(y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+16} \lor \neg \left(z \leq 4.2 \cdot 10^{+131}\right):\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.42e+16) (not (<= z 4.2e+131)))
   (* y (* z -0.5))
   (+ (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.42e+16) || !(z <= 4.2e+131)) {
		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 <= (-1.42d+16)) .or. (.not. (z <= 4.2d+131))) 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 <= -1.42e+16) || !(z <= 4.2e+131)) {
		tmp = y * (z * -0.5);
	} else {
		tmp = (0.125 * x) + t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.42e+16) or not (z <= 4.2e+131):
		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 <= -1.42e+16) || !(z <= 4.2e+131))
		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 <= -1.42e+16) || ~((z <= 4.2e+131)))
		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, -1.42e+16], N[Not[LessEqual[z, 4.2e+131]], $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 < -1.42e16 or 4.19999999999999971e131 < 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 y around inf 66.0%

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

      1. *-commutative 66.0%

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

      2. associate-*r* 66.8%

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

   7. Simplified 66.8%

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

   if -1.42e16 < z < 4.19999999999999971e131

   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 0 79.4%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+16} \lor \neg \left(z \leq 4.2 \cdot 10^{+131}\right):\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+52} \lor \neg \left(x \leq 9.5 \cdot 10^{+136}\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.8e+52) (not (<= x 9.5e+136))) (* 0.125 x) (* y (* z -0.5))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.8e+52) || !(x <= 9.5e+136)) {
		tmp = 0.125 * x;
	} 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 ((x <= (-8.8d+52)) .or. (.not. (x <= 9.5d+136))) then
        tmp = 0.125d0 * x
    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 ((x <= -8.8e+52) || !(x <= 9.5e+136)) {
		tmp = 0.125 * x;
	} else {
		tmp = y * (z * -0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.8e+52) or not (x <= 9.5e+136):
		tmp = 0.125 * x
	else:
		tmp = y * (z * -0.5)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.8e+52) || !(x <= 9.5e+136))
		tmp = Float64(0.125 * x);
	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 ((x <= -8.8e+52) || ~((x <= 9.5e+136)))
		tmp = 0.125 * x;
	else
		tmp = y * (z * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.8e+52], N[Not[LessEqual[x, 9.5e+136]], $MachinePrecision]], N[(0.125 * x), $MachinePrecision], N[(y * N[(z * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.7999999999999999e52 or 9.49999999999999907e136 < 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 70.1%

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

   if -8.7999999999999999e52 < x < 9.49999999999999907e136

   1. Initial program 99.5%

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

      1. associate-+l- 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-+l- 99.5%

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

      4. metadata-eval 99.5%

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

      5. *-commutative 99.5%

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

      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 52.7%

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

      1. *-commutative 52.7%

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

      2. associate-*r* 53.2%

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

   7. Simplified 53.2%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+52} \lor \neg \left(x \leq 9.5 \cdot 10^{+136}\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+43} \lor \neg \left(x \leq 2.75 \cdot 10^{+143}\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.7e+43) (not (<= x 2.75e+143))) (* 0.125 x) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.7e+43) || !(x <= 2.75e+143)) {
		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 <= (-1.7d+43)) .or. (.not. (x <= 2.75d+143))) 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 <= -1.7e+43) || !(x <= 2.75e+143)) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.7e+43) or not (x <= 2.75e+143):
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.7e+43) || !(x <= 2.75e+143))
		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 <= -1.7e+43) || ~((x <= 2.75e+143)))
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.7e+43], N[Not[LessEqual[x, 2.75e+143]], $MachinePrecision]], N[(0.125 * x), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -1.70000000000000006e43 or 2.74999999999999985e143 < 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 69.3%

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

   if -1.70000000000000006e43 < x < 2.74999999999999985e143

   1. Initial program 99.5%

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

      1. associate-+l- 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-+l- 99.5%

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

      4. metadata-eval 99.5%

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

      5. *-commutative 99.5%

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

      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 39.3%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+43} \lor \neg \left(x \leq 2.75 \cdot 10^{+143}\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 33.3% 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 30.8%

   \[\leadsto \color{blue}{t} \]
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 2024116 
(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))