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

Percentage Accurate: 100.0% → 100.0%

Time: 7.3s

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: 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

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

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: 49.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z \cdot -0.5\right)\\ \mathbf{if}\;t \leq -2100000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-252}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+25}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* z -0.5))))
   (if (<= t -2100000000000.0)
     t
     (if (<= t -8.6e-24)
       t_1
       (if (<= t 3.1e-252)
         (* 0.125 x)
         (if (<= t 8.2e-235) t_1 (if (<= t 1.7e+25) (* 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 <= -2100000000000.0) {
		tmp = t;
	} else if (t <= -8.6e-24) {
		tmp = t_1;
	} else if (t <= 3.1e-252) {
		tmp = 0.125 * x;
	} else if (t <= 8.2e-235) {
		tmp = t_1;
	} else if (t <= 1.7e+25) {
		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 <= (-2100000000000.0d0)) then
        tmp = t
    else if (t <= (-8.6d-24)) then
        tmp = t_1
    else if (t <= 3.1d-252) then
        tmp = 0.125d0 * x
    else if (t <= 8.2d-235) then
        tmp = t_1
    else if (t <= 1.7d+25) 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 <= -2100000000000.0) {
		tmp = t;
	} else if (t <= -8.6e-24) {
		tmp = t_1;
	} else if (t <= 3.1e-252) {
		tmp = 0.125 * x;
	} else if (t <= 8.2e-235) {
		tmp = t_1;
	} else if (t <= 1.7e+25) {
		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 <= -2100000000000.0:
		tmp = t
	elif t <= -8.6e-24:
		tmp = t_1
	elif t <= 3.1e-252:
		tmp = 0.125 * x
	elif t <= 8.2e-235:
		tmp = t_1
	elif t <= 1.7e+25:
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z * -0.5))
	tmp = 0.0
	if (t <= -2100000000000.0)
		tmp = t;
	elseif (t <= -8.6e-24)
		tmp = t_1;
	elseif (t <= 3.1e-252)
		tmp = Float64(0.125 * x);
	elseif (t <= 8.2e-235)
		tmp = t_1;
	elseif (t <= 1.7e+25)
		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 <= -2100000000000.0)
		tmp = t;
	elseif (t <= -8.6e-24)
		tmp = t_1;
	elseif (t <= 3.1e-252)
		tmp = 0.125 * x;
	elseif (t <= 8.2e-235)
		tmp = t_1;
	elseif (t <= 1.7e+25)
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z * -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2100000000000.0], t, If[LessEqual[t, -8.6e-24], t$95$1, If[LessEqual[t, 3.1e-252], N[(0.125 * x), $MachinePrecision], If[LessEqual[t, 8.2e-235], t$95$1, If[LessEqual[t, 1.7e+25], N[(0.125 * x), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1e12 or 1.69999999999999992e25 < 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. metadata-eval 100.0%

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

      2. 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 57.1%

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

   if -2.1e12 < t < -8.6000000000000006e-24 or 3.0999999999999998e-252 < t < 8.19999999999999993e-235

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 100.0%

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

   6. Taylor expanded in t around 0 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-*l* 87.0%

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

      3. *-commutative 87.0%

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

   8. Simplified 87.0%

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

   if -8.6000000000000006e-24 < t < 3.0999999999999998e-252 or 8.19999999999999993e-235 < t < 1.69999999999999992e25

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. 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 88.5%

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

   6. Taylor expanded in x around inf 59.4%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2100000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-252}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-235}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+25}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+185} \lor \neg \left(y \leq -1.25 \cdot 10^{+141} \lor \neg \left(y \leq -2.4 \cdot 10^{+123}\right) \land y \leq 8 \cdot 10^{-43}\right):\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.26e+185)
         (not
          (or (<= y -1.25e+141) (and (not (<= y -2.4e+123)) (<= y 8e-43)))))
   (* y (* z -0.5))
   (+ (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.26e+185) || !((y <= -1.25e+141) || (!(y <= -2.4e+123) && (y <= 8e-43)))) {
		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 <= (-1.26d+185)) .or. (.not. (y <= (-1.25d+141)) .or. (.not. (y <= (-2.4d+123))) .and. (y <= 8d-43))) 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 <= -1.26e+185) || !((y <= -1.25e+141) || (!(y <= -2.4e+123) && (y <= 8e-43)))) {
		tmp = y * (z * -0.5);
	} else {
		tmp = (0.125 * x) + t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.26e+185) or not ((y <= -1.25e+141) or (not (y <= -2.4e+123) and (y <= 8e-43))):
		tmp = y * (z * -0.5)
	else:
		tmp = (0.125 * x) + t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.26e+185) || !((y <= -1.25e+141) || (!(y <= -2.4e+123) && (y <= 8e-43))))
		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 ((y <= -1.26e+185) || ~(((y <= -1.25e+141) || (~((y <= -2.4e+123)) && (y <= 8e-43)))))
		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[y, -1.26e+185], N[Not[Or[LessEqual[y, -1.25e+141], And[N[Not[LessEqual[y, -2.4e+123]], $MachinePrecision], LessEqual[y, 8e-43]]]], $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 y < -1.26e185 or -1.25000000000000006e141 < y < -2.39999999999999989e123 or 8.00000000000000062e-43 < y

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. 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 76.2%

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

   6. Taylor expanded in t around 0 57.8%

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

      1. *-commutative 57.8%

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

      2. associate-*l* 57.8%

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

      3. *-commutative 57.8%

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

   8. Simplified 57.8%

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

   if -1.26e185 < y < -1.25000000000000006e141 or -2.39999999999999989e123 < y < 8.00000000000000062e-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. metadata-eval 100.0%

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

      2. 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 inf 85.3%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+185} \lor \neg \left(y \leq -1.25 \cdot 10^{+141} \lor \neg \left(y \leq -2.4 \cdot 10^{+123}\right) \land y \leq 8 \cdot 10^{-43}\right):\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot z\right) \cdot 0.5\\ \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+97}:\\ \;\;\;\;t - t\_1\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+115}:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* y z) 0.5)))
   (if (<= (* y z) -5e+97)
     (- t t_1)
     (if (<= (* y z) 5e+115) (+ (* 0.125 x) t) (- (* 0.125 x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) * 0.5;
	double tmp;
	if ((y * z) <= -5e+97) {
		tmp = t - t_1;
	} else if ((y * z) <= 5e+115) {
		tmp = (0.125 * x) + t;
	} else {
		tmp = (0.125 * x) - 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 = (y * z) * 0.5d0
    if ((y * z) <= (-5d+97)) then
        tmp = t - t_1
    else if ((y * z) <= 5d+115) then
        tmp = (0.125d0 * x) + t
    else
        tmp = (0.125d0 * x) - t_1
    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 ((y * z) <= -5e+97) {
		tmp = t - t_1;
	} else if ((y * z) <= 5e+115) {
		tmp = (0.125 * x) + t;
	} else {
		tmp = (0.125 * x) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) * 0.5
	tmp = 0
	if (y * z) <= -5e+97:
		tmp = t - t_1
	elif (y * z) <= 5e+115:
		tmp = (0.125 * x) + t
	else:
		tmp = (0.125 * x) - t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) * 0.5)
	tmp = 0.0
	if (Float64(y * z) <= -5e+97)
		tmp = Float64(t - t_1);
	elseif (Float64(y * z) <= 5e+115)
		tmp = Float64(Float64(0.125 * x) + t);
	else
		tmp = Float64(Float64(0.125 * x) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) * 0.5;
	tmp = 0.0;
	if ((y * z) <= -5e+97)
		tmp = t - t_1;
	elseif ((y * z) <= 5e+115)
		tmp = (0.125 * x) + t;
	else
		tmp = (0.125 * x) - t_1;
	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[N[(y * z), $MachinePrecision], -5e+97], N[(t - t$95$1), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 5e+115], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -4.99999999999999999e97

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

      2. 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 92.3%

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

   if -4.99999999999999999e97 < (*.f64 y z) < 5.00000000000000008e115

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. 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 inf 92.0%

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

   if 5.00000000000000008e115 < (*.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. metadata-eval 100.0%

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

      2. 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 t around 0 95.6%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+97}:\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+115}:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x - \left(y \cdot z\right) \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+97} \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+63}\right):\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -5e+97) (not (<= (* y z) 2e+63)))
   (- 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+97) || !((y * z) <= 2e+63)) {
		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+97)) .or. (.not. ((y * z) <= 2d+63))) 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+97) || !((y * z) <= 2e+63)) {
		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+97) or not ((y * z) <= 2e+63):
		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+97) || !(Float64(y * z) <= 2e+63))
		tmp = Float64(t - 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) <= -5e+97) || ~(((y * z) <= 2e+63)))
		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+97], N[Not[LessEqual[N[(y * z), $MachinePrecision], 2e+63]], $MachinePrecision]], N[(t - N[(N[(y * z), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -4.99999999999999999e97 or 2.00000000000000012e63 < (*.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. metadata-eval 100.0%

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

      2. 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 87.8%

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

   if -4.99999999999999999e97 < (*.f64 y z) < 2.00000000000000012e63

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. 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 inf 93.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+97} \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+63}\right):\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+25}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.7e-36) t (if (<= t 6.7e+25) (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.7e-36) {
		tmp = t;
	} else if (t <= 6.7e+25) {
		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 <= (-2.7d-36)) then
        tmp = t
    else if (t <= 6.7d+25) 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 <= -2.7e-36) {
		tmp = t;
	} else if (t <= 6.7e+25) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.7e-36:
		tmp = t
	elif t <= 6.7e+25:
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.7e-36)
		tmp = t;
	elseif (t <= 6.7e+25)
		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 <= -2.7e-36)
		tmp = t;
	elseif (t <= 6.7e+25)
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.7e-36], t, If[LessEqual[t, 6.7e+25], N[(0.125 * x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if t < -2.70000000000000007e-36 or 6.70000000000000037e25 < 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. metadata-eval 100.0%

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

      2. 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 54.3%

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

   if -2.70000000000000007e-36 < t < 6.70000000000000037e25

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. 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 90.3%

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

   6. Taylor expanded in x around inf 57.6%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+25}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
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. metadata-eval 100.0%

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

   2. 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: 32.4% 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. metadata-eval 100.0%

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

   2. 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 36.2%

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

6. Final simplification 36.2%

   \[\leadsto t \]
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 2024041 
(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))