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

Percentage Accurate: 100.0% → 100.0%

Time: 5.8s

Alternatives: 7

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.2× speedup

Math

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

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. Final simplification 100.0%

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

Alternative 2: 47.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y \cdot -0.5\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-246}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-304}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-119}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 13500000000000:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+53}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+57}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+80} \lor \neg \left(z \leq 6.2 \cdot 10^{+107}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (* y -0.5))))
   (if (<= z -1.1e-150)
     t_1
     (if (<= z -6e-246)
       (* 0.125 x)
       (if (<= z 2.5e-304)
         t
         (if (<= z 6e-119)
           (* 0.125 x)
           (if (<= z 1.05e-25)
             t
             (if (<= z 13500000000000.0)
               (* 0.125 x)
               (if (<= z 7.5e+53)
                 t
                 (if (<= z 2.8e+57)
                   (* 0.125 x)
                   (if (or (<= z 6.2e+80) (not (<= z 6.2e+107)))
                     t_1
                     t)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y * -0.5);
	double tmp;
	if (z <= -1.1e-150) {
		tmp = t_1;
	} else if (z <= -6e-246) {
		tmp = 0.125 * x;
	} else if (z <= 2.5e-304) {
		tmp = t;
	} else if (z <= 6e-119) {
		tmp = 0.125 * x;
	} else if (z <= 1.05e-25) {
		tmp = t;
	} else if (z <= 13500000000000.0) {
		tmp = 0.125 * x;
	} else if (z <= 7.5e+53) {
		tmp = t;
	} else if (z <= 2.8e+57) {
		tmp = 0.125 * x;
	} else if ((z <= 6.2e+80) || !(z <= 6.2e+107)) {
		tmp = t_1;
	} 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 = z * (y * (-0.5d0))
    if (z <= (-1.1d-150)) then
        tmp = t_1
    else if (z <= (-6d-246)) then
        tmp = 0.125d0 * x
    else if (z <= 2.5d-304) then
        tmp = t
    else if (z <= 6d-119) then
        tmp = 0.125d0 * x
    else if (z <= 1.05d-25) then
        tmp = t
    else if (z <= 13500000000000.0d0) then
        tmp = 0.125d0 * x
    else if (z <= 7.5d+53) then
        tmp = t
    else if (z <= 2.8d+57) then
        tmp = 0.125d0 * x
    else if ((z <= 6.2d+80) .or. (.not. (z <= 6.2d+107))) then
        tmp = t_1
    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 = z * (y * -0.5);
	double tmp;
	if (z <= -1.1e-150) {
		tmp = t_1;
	} else if (z <= -6e-246) {
		tmp = 0.125 * x;
	} else if (z <= 2.5e-304) {
		tmp = t;
	} else if (z <= 6e-119) {
		tmp = 0.125 * x;
	} else if (z <= 1.05e-25) {
		tmp = t;
	} else if (z <= 13500000000000.0) {
		tmp = 0.125 * x;
	} else if (z <= 7.5e+53) {
		tmp = t;
	} else if (z <= 2.8e+57) {
		tmp = 0.125 * x;
	} else if ((z <= 6.2e+80) || !(z <= 6.2e+107)) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y * -0.5)
	tmp = 0
	if z <= -1.1e-150:
		tmp = t_1
	elif z <= -6e-246:
		tmp = 0.125 * x
	elif z <= 2.5e-304:
		tmp = t
	elif z <= 6e-119:
		tmp = 0.125 * x
	elif z <= 1.05e-25:
		tmp = t
	elif z <= 13500000000000.0:
		tmp = 0.125 * x
	elif z <= 7.5e+53:
		tmp = t
	elif z <= 2.8e+57:
		tmp = 0.125 * x
	elif (z <= 6.2e+80) or not (z <= 6.2e+107):
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y * -0.5))
	tmp = 0.0
	if (z <= -1.1e-150)
		tmp = t_1;
	elseif (z <= -6e-246)
		tmp = Float64(0.125 * x);
	elseif (z <= 2.5e-304)
		tmp = t;
	elseif (z <= 6e-119)
		tmp = Float64(0.125 * x);
	elseif (z <= 1.05e-25)
		tmp = t;
	elseif (z <= 13500000000000.0)
		tmp = Float64(0.125 * x);
	elseif (z <= 7.5e+53)
		tmp = t;
	elseif (z <= 2.8e+57)
		tmp = Float64(0.125 * x);
	elseif ((z <= 6.2e+80) || !(z <= 6.2e+107))
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y * -0.5);
	tmp = 0.0;
	if (z <= -1.1e-150)
		tmp = t_1;
	elseif (z <= -6e-246)
		tmp = 0.125 * x;
	elseif (z <= 2.5e-304)
		tmp = t;
	elseif (z <= 6e-119)
		tmp = 0.125 * x;
	elseif (z <= 1.05e-25)
		tmp = t;
	elseif (z <= 13500000000000.0)
		tmp = 0.125 * x;
	elseif (z <= 7.5e+53)
		tmp = t;
	elseif (z <= 2.8e+57)
		tmp = 0.125 * x;
	elseif ((z <= 6.2e+80) || ~((z <= 6.2e+107)))
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y * -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e-150], t$95$1, If[LessEqual[z, -6e-246], N[(0.125 * x), $MachinePrecision], If[LessEqual[z, 2.5e-304], t, If[LessEqual[z, 6e-119], N[(0.125 * x), $MachinePrecision], If[LessEqual[z, 1.05e-25], t, If[LessEqual[z, 13500000000000.0], N[(0.125 * x), $MachinePrecision], If[LessEqual[z, 7.5e+53], t, If[LessEqual[z, 2.8e+57], N[(0.125 * x), $MachinePrecision], If[Or[LessEqual[z, 6.2e+80], N[Not[LessEqual[z, 6.2e+107]], $MachinePrecision]], t$95$1, t]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e-150 or 2.8e57 < z < 6.19999999999999976e80 or 6.20000000000000052e107 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 54.6%

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

      1. *-commutative 54.6%

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

      2. *-commutative 54.6%

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

      3. associate-*r* 54.6%

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

   4. Simplified 54.6%

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

   if -1.1e-150 < z < -6e-246 or 2.49999999999999983e-304 < z < 6.0000000000000004e-119 or 1.05000000000000001e-25 < z < 1.35e13 or 7.4999999999999997e53 < z < 2.8e57

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 55.7%

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

   if -6e-246 < z < 2.49999999999999983e-304 or 6.0000000000000004e-119 < z < 1.05000000000000001e-25 or 1.35e13 < z < 7.4999999999999997e53 or 6.19999999999999976e80 < z < 6.20000000000000052e107

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 50.8%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-246}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-304}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-119}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 13500000000000:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+53}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+57}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+80} \lor \neg \left(z \leq 6.2 \cdot 10^{+107}\right):\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 87.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{-25} \lor \neg \left(y \cdot z \leq 20000000000000\right):\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -5e-25) (not (<= (* y z) 20000000000000.0)))
   (- 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-25) || !((y * z) <= 20000000000000.0)) {
		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-25)) .or. (.not. ((y * z) <= 20000000000000.0d0))) 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-25) || !((y * z) <= 20000000000000.0)) {
		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-25) or not ((y * z) <= 20000000000000.0):
		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-25) || !(Float64(y * z) <= 20000000000000.0))
		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-25) || ~(((y * z) <= 20000000000000.0)))
		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-25], N[Not[LessEqual[N[(y * z), $MachinePrecision], 20000000000000.0]], $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) < -4.99999999999999962e-25 or 2e13 < (*.f64 y z)

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 87.0%

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

   if -4.99999999999999962e-25 < (*.f64 y z) < 2e13

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 92.5%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{-25} \lor \neg \left(y \cdot z \leq 20000000000000\right):\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]

Alternative 4: 88.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot z\right) \cdot 0.5\\ \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+35}:\\ \;\;\;\;0.125 \cdot x - t_1\\ \mathbf{elif}\;y \cdot z \leq 20000000000000:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* y z) 0.5)))
   (if (<= (* y z) -5e+35)
     (- (* 0.125 x) t_1)
     (if (<= (* y z) 20000000000000.0) (+ (* 0.125 x) t) (- t 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+35) {
		tmp = (0.125 * x) - t_1;
	} else if ((y * z) <= 20000000000000.0) {
		tmp = (0.125 * x) + t;
	} else {
		tmp = t - 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+35)) then
        tmp = (0.125d0 * x) - t_1
    else if ((y * z) <= 20000000000000.0d0) then
        tmp = (0.125d0 * x) + t
    else
        tmp = t - 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+35) {
		tmp = (0.125 * x) - t_1;
	} else if ((y * z) <= 20000000000000.0) {
		tmp = (0.125 * x) + t;
	} else {
		tmp = t - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) * 0.5
	tmp = 0
	if (y * z) <= -5e+35:
		tmp = (0.125 * x) - t_1
	elif (y * z) <= 20000000000000.0:
		tmp = (0.125 * x) + t
	else:
		tmp = t - 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+35)
		tmp = Float64(Float64(0.125 * x) - t_1);
	elseif (Float64(y * z) <= 20000000000000.0)
		tmp = Float64(Float64(0.125 * x) + t);
	else
		tmp = Float64(t - 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+35)
		tmp = (0.125 * x) - t_1;
	elseif ((y * z) <= 20000000000000.0)
		tmp = (0.125 * x) + t;
	else
		tmp = t - 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+35], N[(N[(0.125 * x), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 20000000000000.0], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision], N[(t - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5.00000000000000021e35

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 98.3%

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

   if -5.00000000000000021e35 < (*.f64 y z) < 2e13

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.5%

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

   if 2e13 < (*.f64 y z)

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 87.0%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+35}:\\ \;\;\;\;0.125 \cdot x - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{elif}\;y \cdot z \leq 20000000000000:\\ \;\;\;\;0.125 \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \end{array} \]

Alternative 5: 69.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{-81} \lor \neg \left(z \leq 1.4 \cdot 10^{+116}\right):\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.46e-81) (not (<= z 1.4e+116)))
   (* z (* y -0.5))
   (+ (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.46e-81) || !(z <= 1.4e+116)) {
		tmp = 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 ((z <= (-1.46d-81)) .or. (.not. (z <= 1.4d+116))) then
        tmp = 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 ((z <= -1.46e-81) || !(z <= 1.4e+116)) {
		tmp = z * (y * -0.5);
	} else {
		tmp = (0.125 * x) + t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.46e-81) or not (z <= 1.4e+116):
		tmp = z * (y * -0.5)
	else:
		tmp = (0.125 * x) + t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.46e-81) || !(z <= 1.4e+116))
		tmp = 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 ((z <= -1.46e-81) || ~((z <= 1.4e+116)))
		tmp = z * (y * -0.5);
	else
		tmp = (0.125 * x) + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.46e-81], N[Not[LessEqual[z, 1.4e+116]], $MachinePrecision]], N[(z * N[(y * -0.5), $MachinePrecision]), $MachinePrecision], N[(N[(0.125 * x), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4599999999999999e-81 or 1.40000000000000002e116 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 58.8%

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

      1. *-commutative 58.8%

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

      2. *-commutative 58.8%

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

      3. associate-*r* 58.8%

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

   4. Simplified 58.8%

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

   if -1.4599999999999999e-81 < z < 1.40000000000000002e116

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.0%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{-81} \lor \neg \left(z \leq 1.4 \cdot 10^{+116}\right):\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x + t\\ \end{array} \]

Alternative 6: 48.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-52}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-28}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.3e-52) t (if (<= t 8e-28) (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.3e-52) {
		tmp = t;
	} else if (t <= 8e-28) {
		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 <= (-3.3d-52)) then
        tmp = t
    else if (t <= 8d-28) 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 <= -3.3e-52) {
		tmp = t;
	} else if (t <= 8e-28) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.3e-52:
		tmp = t
	elif t <= 8e-28:
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.3e-52)
		tmp = t;
	elseif (t <= 8e-28)
		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 <= -3.3e-52)
		tmp = t;
	elseif (t <= 8e-28)
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.3e-52], t, If[LessEqual[t, 8e-28], N[(0.125 * x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if t < -3.29999999999999995e-52 or 7.99999999999999977e-28 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 50.2%

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

   if -3.29999999999999995e-52 < t < 7.99999999999999977e-28

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 52.9%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-52}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-28}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 33.2% 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. Taylor expanded in t around inf 29.8%

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

3. Final simplification 29.8%

   \[\leadsto t \]

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 2023279 
(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))