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

Percentage Accurate: 100.0% → 100.0%

Time: 3.7s

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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   2. associate-+l+ 100.0%

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

   3. fma-def 100.0%

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

   4. metadata-eval 100.0%

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

   5. distribute-frac-neg 100.0%

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

   6. distribute-lft-neg-out 100.0%

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

   7. associate-*l/ 100.0%

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

   8. fma-def 100.0%

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

   9. neg-mul-1 100.0%

      \[\leadsto \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot y}}{2}, z, t\right)\right) \]

   10. *-commutative 100.0%

       \[\leadsto \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(\frac{\color{blue}{y \cdot -1}}{2}, z, t\right)\right) \]

   11. associate-/l* 100.0%

       \[\leadsto \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(\color{blue}{\frac{y}{\frac{2}{-1}}}, z, t\right)\right) \]

   12. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(\frac{y}{-2}, z, t\right)\right) \]

Alternative 2: 51.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot z\right) \cdot -0.5\\ \mathbf{if}\;x \leq -5 \cdot 10^{+79}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-92}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-300}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* y z) -0.5)))
   (if (<= x -5e+79)
     (* 0.125 x)
     (if (<= x -1.2e-92)
       t
       (if (<= x -9.2e-265)
         t_1
         (if (<= x -2.5e-300) t (if (<= x 1.15e+154) t_1 (* 0.125 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) * -0.5;
	double tmp;
	if (x <= -5e+79) {
		tmp = 0.125 * x;
	} else if (x <= -1.2e-92) {
		tmp = t;
	} else if (x <= -9.2e-265) {
		tmp = t_1;
	} else if (x <= -2.5e-300) {
		tmp = t;
	} else if (x <= 1.15e+154) {
		tmp = t_1;
	} else {
		tmp = 0.125 * x;
	}
	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 (x <= (-5d+79)) then
        tmp = 0.125d0 * x
    else if (x <= (-1.2d-92)) then
        tmp = t
    else if (x <= (-9.2d-265)) then
        tmp = t_1
    else if (x <= (-2.5d-300)) then
        tmp = t
    else if (x <= 1.15d+154) then
        tmp = t_1
    else
        tmp = 0.125d0 * x
    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 (x <= -5e+79) {
		tmp = 0.125 * x;
	} else if (x <= -1.2e-92) {
		tmp = t;
	} else if (x <= -9.2e-265) {
		tmp = t_1;
	} else if (x <= -2.5e-300) {
		tmp = t;
	} else if (x <= 1.15e+154) {
		tmp = t_1;
	} else {
		tmp = 0.125 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) * -0.5
	tmp = 0
	if x <= -5e+79:
		tmp = 0.125 * x
	elif x <= -1.2e-92:
		tmp = t
	elif x <= -9.2e-265:
		tmp = t_1
	elif x <= -2.5e-300:
		tmp = t
	elif x <= 1.15e+154:
		tmp = t_1
	else:
		tmp = 0.125 * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) * -0.5)
	tmp = 0.0
	if (x <= -5e+79)
		tmp = Float64(0.125 * x);
	elseif (x <= -1.2e-92)
		tmp = t;
	elseif (x <= -9.2e-265)
		tmp = t_1;
	elseif (x <= -2.5e-300)
		tmp = t;
	elseif (x <= 1.15e+154)
		tmp = t_1;
	else
		tmp = Float64(0.125 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) * -0.5;
	tmp = 0.0;
	if (x <= -5e+79)
		tmp = 0.125 * x;
	elseif (x <= -1.2e-92)
		tmp = t;
	elseif (x <= -9.2e-265)
		tmp = t_1;
	elseif (x <= -2.5e-300)
		tmp = t;
	elseif (x <= 1.15e+154)
		tmp = t_1;
	else
		tmp = 0.125 * x;
	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[x, -5e+79], N[(0.125 * x), $MachinePrecision], If[LessEqual[x, -1.2e-92], t, If[LessEqual[x, -9.2e-265], t$95$1, If[LessEqual[x, -2.5e-300], t, If[LessEqual[x, 1.15e+154], t$95$1, N[(0.125 * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5e79 or 1.15e154 < x

   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 69.7%

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

   if -5e79 < x < -1.2000000000000001e-92 or -9.1999999999999996e-265 < x < -2.49999999999999998e-300

   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 58.1%

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

   if -1.2000000000000001e-92 < x < -9.1999999999999996e-265 or -2.49999999999999998e-300 < x < 1.15e154

   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 62.6%

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

      1. *-commutative 62.6%

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

   4. Simplified 62.6%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+79}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-92}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-265}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-300}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+154}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \]

Alternative 3: 82.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2.1 \cdot 10^{+104} \lor \neg \left(y \cdot z \leq 4.8 \cdot 10^{+195}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* y z) -2.1e+104) (not (<= (* y z) 4.8e+195)))
   (* (* y z) -0.5)
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -2.1e+104) || !((y * z) <= 4.8e+195)) {
		tmp = (y * z) * -0.5;
	} else {
		tmp = t + (0.125 * x);
	}
	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) <= (-2.1d+104)) .or. (.not. ((y * z) <= 4.8d+195))) then
        tmp = (y * z) * (-0.5d0)
    else
        tmp = t + (0.125d0 * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y * z) <= -2.1e+104) || !((y * z) <= 4.8e+195)) {
		tmp = (y * z) * -0.5;
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y * z) <= -2.1e+104) or not ((y * z) <= 4.8e+195):
		tmp = (y * z) * -0.5
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y * z) <= -2.1e+104) || !(Float64(y * z) <= 4.8e+195))
		tmp = Float64(Float64(y * z) * -0.5);
	else
		tmp = Float64(t + Float64(0.125 * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y * z) <= -2.1e+104) || ~(((y * z) <= 4.8e+195)))
		tmp = (y * z) * -0.5;
	else
		tmp = t + (0.125 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -2.1e+104], N[Not[LessEqual[N[(y * z), $MachinePrecision], 4.8e+195]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * -0.5), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2.0999999999999998e104 or 4.8000000000000005e195 < (*.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 y around inf 88.6%

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

      1. *-commutative 88.6%

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

   4. Simplified 88.6%

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

   if -2.0999999999999998e104 < (*.f64 y z) < 4.8000000000000005e195

   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 82.0%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2.1 \cdot 10^{+104} \lor \neg \left(y \cdot z \leq 4.8 \cdot 10^{+195}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]

Alternative 4: 82.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+119} \lor \neg \left(x \leq 1.02 \cdot 10^{+154}\right):\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.25e+119) (not (<= x 1.02e+154)))
   (+ t (* 0.125 x))
   (- t (* (* y z) 0.5))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.25e+119) || !(x <= 1.02e+154)) {
		tmp = t + (0.125 * x);
	} else {
		tmp = t - ((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 <= (-2.25d+119)) .or. (.not. (x <= 1.02d+154))) then
        tmp = t + (0.125d0 * x)
    else
        tmp = t - ((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 <= -2.25e+119) || !(x <= 1.02e+154)) {
		tmp = t + (0.125 * x);
	} else {
		tmp = t - ((y * z) * 0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.25e+119) or not (x <= 1.02e+154):
		tmp = t + (0.125 * x)
	else:
		tmp = t - ((y * z) * 0.5)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.25e+119) || !(x <= 1.02e+154))
		tmp = Float64(t + Float64(0.125 * x));
	else
		tmp = Float64(t - Float64(Float64(y * z) * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.25e+119) || ~((x <= 1.02e+154)))
		tmp = t + (0.125 * x);
	else
		tmp = t - ((y * z) * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.25e+119], N[Not[LessEqual[x, 1.02e+154]], $MachinePrecision]], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(y * z), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2500000000000001e119 or 1.02000000000000007e154 < x

   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 85.9%

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

   if -2.2500000000000001e119 < x < 1.02000000000000007e154

   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 88.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+119} \lor \neg \left(x \leq 1.02 \cdot 10^{+154}\right):\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \end{array} \]

Alternative 5: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 * z) / 2.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 6: 50.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+79}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.4e+79) (* 0.125 x) (if (<= x 3e+43) t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.4e+79) {
		tmp = 0.125 * x;
	} else if (x <= 3e+43) {
		tmp = t;
	} else {
		tmp = 0.125 * x;
	}
	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 <= (-2.4d+79)) then
        tmp = 0.125d0 * x
    else if (x <= 3d+43) then
        tmp = t
    else
        tmp = 0.125d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.4e+79) {
		tmp = 0.125 * x;
	} else if (x <= 3e+43) {
		tmp = t;
	} else {
		tmp = 0.125 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.4e+79:
		tmp = 0.125 * x
	elif x <= 3e+43:
		tmp = t
	else:
		tmp = 0.125 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.4e+79)
		tmp = Float64(0.125 * x);
	elseif (x <= 3e+43)
		tmp = t;
	else
		tmp = Float64(0.125 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.4e+79)
		tmp = 0.125 * x;
	elseif (x <= 3e+43)
		tmp = t;
	else
		tmp = 0.125 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.4e+79], N[(0.125 * x), $MachinePrecision], If[LessEqual[x, 3e+43], t, N[(0.125 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.39999999999999986e79 or 3.00000000000000017e43 < x

   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 63.4%

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

   if -2.39999999999999986e79 < x < 3.00000000000000017e43

   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 43.0%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+79}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \]

Alternative 7: 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. Taylor expanded in t around inf 30.8%

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

3. Final simplification 30.8%

   \[\leadsto t \]

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 2023293 
(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))