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

Percentage Accurate: 100.0% → 100.0%

Time: 6.1s

Alternatives: 5

Speedup: 2.2×

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, 2.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z \cdot -0.5, y, \mathsf{fma}\left(0.125, x, t\right)\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma (* z -0.5) y (fma 0.125 x t)))

C

double code(double x, double y, double z, double t) {
	return fma((z * -0.5), y, fma(0.125, x, t));
}

Julia

function code(x, y, z, t)
	return fma(Float64(z * -0.5), y, fma(0.125, x, t))
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(z * -0.5), $MachinePrecision] * y + N[(0.125 * x + t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

   4. associate-/l* N/A

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

   5. *-commutative N/A

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

   6. distribute-lft-neg-in N/A

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

   7. +-commutative N/A

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

   8. accelerator-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\frac{z}{2}\right)\right), \color{blue}{y}, \left(t + \frac{1}{8} \cdot x\right)\right) \]

   9. div-inv N/A

      \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(z \cdot \frac{1}{2}\right)\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

   10. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{fma.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

   11. metadata-eval N/A

       \[\leadsto \mathsf{fma.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

   12. metadata-eval N/A

       \[\leadsto \mathsf{fma.f64}\left(\left(z \cdot \frac{-1}{2}\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{fma.f64}\left(\left(z \cdot \frac{1}{-2}\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

   14. metadata-eval N/A

       \[\leadsto \mathsf{fma.f64}\left(\left(z \cdot \frac{1}{\mathsf{neg}\left(2\right)}\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

   15. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \left(\frac{1}{\mathsf{neg}\left(2\right)}\right)\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

   16. metadata-eval N/A

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \left(\frac{1}{-2}\right)\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

   17. metadata-eval N/A

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

   18. +-commutative N/A

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), y, \left(\frac{1}{8} \cdot x + t\right)\right) \]

   19. accelerator-lowering-fma.f64 N/A

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), y, \mathsf{fma.f64}\left(\left(\frac{1}{8}\right), x, t\right)\right) \]

   20. metadata-eval 100.0%

       \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), y, \mathsf{fma.f64}\left(\frac{1}{8}, x, t\right)\right) \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot -0.5, y, \mathsf{fma}\left(0.125, x, t\right)\right)} \]
5. Add Preprocessing

Alternative 2: 80.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z \cdot -0.5, y, t\right)\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(0.125, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (* z -0.5) y t)))
   (if (<= z -1.65e-77) t_1 (if (<= z 1.25e+29) (fma 0.125 x t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((z * -0.5), y, t);
	double tmp;
	if (z <= -1.65e-77) {
		tmp = t_1;
	} else if (z <= 1.25e+29) {
		tmp = fma(0.125, x, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(z * -0.5), y, t)
	tmp = 0.0
	if (z <= -1.65e-77)
		tmp = t_1;
	elseif (z <= 1.25e+29)
		tmp = fma(0.125, x, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * -0.5), $MachinePrecision] * y + t), $MachinePrecision]}, If[LessEqual[z, -1.65e-77], t$95$1, If[LessEqual[z, 1.25e+29], N[(0.125 * x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.64999999999999996e-77 or 1.25e29 < z

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. distribute-lft-neg-in N/A

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

      7. +-commutative N/A

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

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\frac{z}{2}\right)\right), \color{blue}{y}, \left(t + \frac{1}{8} \cdot x\right)\right) \]

      9. div-inv N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(z \cdot \frac{1}{2}\right)\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\left(z \cdot \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\left(z \cdot \frac{-1}{2}\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\left(z \cdot \frac{1}{-2}\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\left(z \cdot \frac{1}{\mathsf{neg}\left(2\right)}\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \left(\frac{1}{\mathsf{neg}\left(2\right)}\right)\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \left(\frac{1}{-2}\right)\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), y, \left(t + \frac{1}{8} \cdot x\right)\right) \]

      18. +-commutative N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), y, \left(\frac{1}{8} \cdot x + t\right)\right) \]

      19. accelerator-lowering-fma.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), y, \mathsf{fma.f64}\left(\left(\frac{1}{8}\right), x, t\right)\right) \]

      20. metadata-eval 100.0%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), y, \mathsf{fma.f64}\left(\frac{1}{8}, x, t\right)\right) \]

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(z, \frac{-1}{2}\right), y, \color{blue}{t}\right) \]
   6. Step-by-step derivation

   7. Simplified 75.5%

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

   if -1.64999999999999996e-77 < z < 1.25e29

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{t + \frac{1}{8} \cdot x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{1}{8} \cdot x + \color{blue}{t} \]

      2. accelerator-lowering-fma.f64 86.1%

         \[\leadsto \mathsf{fma.f64}\left(\frac{1}{8}, \color{blue}{x}, t\right) \]

   5. Simplified 86.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.125, x, t\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 48.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+40}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+146}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.5e+40) (* 0.125 x) (if (<= x 4.5e+146) t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.5e+40) {
		tmp = 0.125 * x;
	} else if (x <= 4.5e+146) {
		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 <= (-4.5d+40)) then
        tmp = 0.125d0 * x
    else if (x <= 4.5d+146) 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 <= -4.5e+40) {
		tmp = 0.125 * x;
	} else if (x <= 4.5e+146) {
		tmp = t;
	} else {
		tmp = 0.125 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.5e+40:
		tmp = 0.125 * x
	elif x <= 4.5e+146:
		tmp = t
	else:
		tmp = 0.125 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.5e+40)
		tmp = Float64(0.125 * x);
	elseif (x <= 4.5e+146)
		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 <= -4.5e+40)
		tmp = 0.125 * x;
	elseif (x <= 4.5e+146)
		tmp = t;
	else
		tmp = 0.125 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.5e+40], N[(0.125 * x), $MachinePrecision], If[LessEqual[x, 4.5e+146], t, N[(0.125 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.50000000000000032e40 or 4.50000000000000026e146 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{8} \cdot x} \]
   4. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto \frac{1}{8} \cdot x + \color{blue}{0} \]

      2. accelerator-lowering-fma.f64 72.8%

         \[\leadsto \mathsf{fma.f64}\left(\frac{1}{8}, \color{blue}{x}, 0\right) \]

   5. Simplified 72.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.125, x, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto \frac{1}{8} \cdot \color{blue}{x} \]

      2. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{\frac{1}{8}} \]

      3. *-lowering-*.f64 72.8%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\frac{1}{8}}\right) \]

   7. Applied egg-rr 72.8%

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

   if -4.50000000000000032e40 < x < 4.50000000000000026e146

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t} \]
   4. Step-by-step derivation

   5. Simplified 41.2%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+40}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+146}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.0% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(0.125, x, t\right) \end{array} \]

FPCore

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

C

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

Julia

function code(x, y, z, t)
	return fma(0.125, x, t)
end

Wolfram

code[x_, y_, z_, t_] := N[(0.125 * x + 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. Taylor expanded in y around 0

   \[\leadsto \color{blue}{t + \frac{1}{8} \cdot x} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \frac{1}{8} \cdot x + \color{blue}{t} \]

   2. accelerator-lowering-fma.f64 63.7%

      \[\leadsto \mathsf{fma.f64}\left(\frac{1}{8}, \color{blue}{x}, t\right) \]

5. Simplified 63.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.125, x, t\right)} \]
6. Add Preprocessing

Alternative 5: 33.0% accurate, 39.0× 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. Add Preprocessing

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{t} \]
4. Step-by-step derivation

5. Simplified 29.9%

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

Developer Target 1: 100.0% accurate, 1.1× 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 2024193 
(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))