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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(0.125 * x + N[(y * N[(z * -0.5), $MachinePrecision] + 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. associate-+l- 100.0%

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

   2. fmm-def 100.0%

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

   3. sub-neg 100.0%

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

   4. distribute-neg-in 100.0%

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

   5. distribute-frac-neg 100.0%

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

   6. distribute-rgt-neg-out 100.0%

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

   7. remove-double-neg 100.0%

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

   8. metadata-eval 100.0%

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

   9. associate-/l* 100.0%

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

   10. fma-define 100.0%

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

   11. neg-mul-1 100.0%

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

   12. *-commutative 100.0%

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

   13. associate-/l* 100.0%

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

   14. metadata-eval 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+19}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-252}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+99}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.22e+19)
   t
   (if (<= t 1.25e-252)
     (* 0.125 x)
     (if (<= t 5.8e-84) (* z (* y -0.5)) (if (<= t 9e+99) (* 0.125 x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.22e+19) {
		tmp = t;
	} else if (t <= 1.25e-252) {
		tmp = 0.125 * x;
	} else if (t <= 5.8e-84) {
		tmp = z * (y * -0.5);
	} else if (t <= 9e+99) {
		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 <= (-1.22d+19)) then
        tmp = t
    else if (t <= 1.25d-252) then
        tmp = 0.125d0 * x
    else if (t <= 5.8d-84) then
        tmp = z * (y * (-0.5d0))
    else if (t <= 9d+99) 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 <= -1.22e+19) {
		tmp = t;
	} else if (t <= 1.25e-252) {
		tmp = 0.125 * x;
	} else if (t <= 5.8e-84) {
		tmp = z * (y * -0.5);
	} else if (t <= 9e+99) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.22e+19:
		tmp = t
	elif t <= 1.25e-252:
		tmp = 0.125 * x
	elif t <= 5.8e-84:
		tmp = z * (y * -0.5)
	elif t <= 9e+99:
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.22e+19)
		tmp = t;
	elseif (t <= 1.25e-252)
		tmp = Float64(0.125 * x);
	elseif (t <= 5.8e-84)
		tmp = Float64(z * Float64(y * -0.5));
	elseif (t <= 9e+99)
		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 <= -1.22e+19)
		tmp = t;
	elseif (t <= 1.25e-252)
		tmp = 0.125 * x;
	elseif (t <= 5.8e-84)
		tmp = z * (y * -0.5);
	elseif (t <= 9e+99)
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.22e+19], t, If[LessEqual[t, 1.25e-252], N[(0.125 * x), $MachinePrecision], If[LessEqual[t, 5.8e-84], N[(z * N[(y * -0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+99], N[(0.125 * x), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.22e19 or 8.9999999999999999e99 < 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. associate-+l- 100.0%

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

      2. fmm-def 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. distribute-frac-neg 100.0%

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

      6. distribute-rgt-neg-out 100.0%

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

      7. remove-double-neg 100.0%

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

      8. metadata-eval 100.0%

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

      9. associate-/l* 100.0%

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

      10. fma-define 100.0%

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

      11. neg-mul-1 100.0%

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

      12. *-commutative 100.0%

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

      13. associate-/l* 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 75.6%

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

   if -1.22e19 < t < 1.25000000000000002e-252 or 5.80000000000000038e-84 < t < 8.9999999999999999e99

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-+l- 100.0%

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

      4. *-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 64.5%

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

   6. Taylor expanded in x around inf 50.8%

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

   if 1.25000000000000002e-252 < t < 5.80000000000000038e-84

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-+l- 100.0%

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

      4. *-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 89.4%

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

   6. Taylor expanded in t around 0 75.1%

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

   7. Taylor expanded in x around 0 64.0%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+19}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-252}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+99}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+18} \lor \neg \left(x \leq 2.45 \cdot 10^{+69}\right):\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.4e+18) (not (<= x 2.45e+69)))
   (+ t (* 0.125 x))
   (- t (* (* y z) 0.5))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.4e+18) || !(x <= 2.45e+69)) {
		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 <= (-7.4d+18)) .or. (.not. (x <= 2.45d+69))) 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 <= -7.4e+18) || !(x <= 2.45e+69)) {
		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 <= -7.4e+18) or not (x <= 2.45e+69):
		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 <= -7.4e+18) || !(x <= 2.45e+69))
		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 <= -7.4e+18) || ~((x <= 2.45e+69)))
		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, -7.4e+18], N[Not[LessEqual[x, 2.45e+69]], $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 < -7.4e18 or 2.45e69 < x

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-+l- 100.0%

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

      4. *-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 83.1%

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

   if -7.4e18 < x < 2.45e69

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-+l- 100.0%

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

      4. *-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 94.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+18} \lor \neg \left(x \leq 2.45 \cdot 10^{+69}\right):\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+110}:\\ \;\;\;\;0.125 \cdot x + -0.5 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+69}:\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.4e+110)
   (+ (* 0.125 x) (* -0.5 (* y z)))
   (if (<= x 2.7e+69) (- t (* (* y z) 0.5)) (+ t (* 0.125 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.4e+110) {
		tmp = (0.125 * x) + (-0.5 * (y * z));
	} else if (x <= 2.7e+69) {
		tmp = t - ((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 (x <= (-4.4d+110)) then
        tmp = (0.125d0 * x) + ((-0.5d0) * (y * z))
    else if (x <= 2.7d+69) then
        tmp = t - ((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 (x <= -4.4e+110) {
		tmp = (0.125 * x) + (-0.5 * (y * z));
	} else if (x <= 2.7e+69) {
		tmp = t - ((y * z) * 0.5);
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.4e+110:
		tmp = (0.125 * x) + (-0.5 * (y * z))
	elif x <= 2.7e+69:
		tmp = t - ((y * z) * 0.5)
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.4e+110)
		tmp = Float64(Float64(0.125 * x) + Float64(-0.5 * Float64(y * z)));
	elseif (x <= 2.7e+69)
		tmp = Float64(t - 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 (x <= -4.4e+110)
		tmp = (0.125 * x) + (-0.5 * (y * z));
	elseif (x <= 2.7e+69)
		tmp = t - ((y * z) * 0.5);
	else
		tmp = t + (0.125 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.4e+110], N[(N[(0.125 * x), $MachinePrecision] + N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+69], N[(t - N[(N[(y * z), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.39999999999999984e110

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-+l- 100.0%

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

      4. *-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 62.2%

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

   6. Taylor expanded in t around 0 56.5%

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

   7. Taylor expanded in z around 0 94.4%

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

   if -4.39999999999999984e110 < x < 2.6999999999999998e69

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-+l- 100.0%

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

      4. *-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 92.8%

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

   if 2.6999999999999998e69 < x

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-+l- 100.0%

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

      4. *-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 82.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+110}:\\ \;\;\;\;0.125 \cdot x + -0.5 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+69}:\\ \;\;\;\;t - \left(y \cdot z\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+181} \lor \neg \left(y \leq 4.9 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.42e+181) (not (<= y 4.9e-14)))
   (* z (* y -0.5))
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.42e+181) || !(y <= 4.9e-14)) {
		tmp = z * (y * -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 <= (-1.42d+181)) .or. (.not. (y <= 4.9d-14))) then
        tmp = z * (y * (-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 <= -1.42e+181) || !(y <= 4.9e-14)) {
		tmp = z * (y * -0.5);
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.42e+181) or not (y <= 4.9e-14):
		tmp = z * (y * -0.5)
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.42e+181) || !(y <= 4.9e-14))
		tmp = Float64(z * Float64(y * -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 <= -1.42e+181) || ~((y <= 4.9e-14)))
		tmp = z * (y * -0.5);
	else
		tmp = t + (0.125 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.42e+181], N[Not[LessEqual[y, 4.9e-14]], $MachinePrecision]], N[(z * N[(y * -0.5), $MachinePrecision]), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4199999999999999e181 or 4.89999999999999995e-14 < 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. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-+l- 100.0%

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

      4. *-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 85.6%

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

   6. Taylor expanded in t around 0 64.3%

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

   7. Taylor expanded in x around 0 56.3%

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

   if -1.4199999999999999e181 < y < 4.89999999999999995e-14

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-+l- 100.0%

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

      4. *-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 83.3%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+181} \lor \neg \left(y \leq 4.9 \cdot 10^{-14}\right):\\ \;\;\;\;z \cdot \left(y \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+109} \lor \neg \left(x \leq 5.3 \cdot 10^{+70}\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.32e+109) (not (<= x 5.3e+70))) (* 0.125 x) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.32e+109) || !(x <= 5.3e+70)) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.32d+109)) .or. (.not. (x <= 5.3d+70))) then
        tmp = 0.125d0 * x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.32e+109) || !(x <= 5.3e+70)) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.32e+109) or not (x <= 5.3e+70):
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.32e+109) || !(x <= 5.3e+70))
		tmp = Float64(0.125 * x);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.32e+109) || ~((x <= 5.3e+70)))
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.32e+109], N[Not[LessEqual[x, 5.3e+70]], $MachinePrecision]], N[(0.125 * x), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -1.32000000000000008e109 or 5.3e70 < x

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-+l- 100.0%

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

      4. *-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 82.5%

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

   6. Taylor expanded in x around inf 66.3%

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

   if -1.32000000000000008e109 < x < 5.3e70

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. fmm-def 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. distribute-frac-neg 100.0%

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

      6. distribute-rgt-neg-out 100.0%

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

      7. remove-double-neg 100.0%

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

      8. metadata-eval 100.0%

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

      9. associate-/l* 100.0%

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

      10. fma-define 100.0%

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

      11. neg-mul-1 100.0%

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

      12. *-commutative 100.0%

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

      13. associate-/l* 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 56.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+109} \lor \neg \left(x \leq 5.3 \cdot 10^{+70}\right):\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.2× speedup

Math

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

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(y * Float64(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[(y * N[(z / 2.0), $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. associate-+l- 100.0%

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

   2. *-commutative 100.0%

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

   3. associate-+l- 100.0%

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

   4. *-commutative 100.0%

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

   5. metadata-eval 100.0%

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

   6. associate-/l* 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 8: 32.8% 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. associate-+l- 100.0%

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

   2. fmm-def 100.0%

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

   3. sub-neg 100.0%

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

   4. distribute-neg-in 100.0%

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

   5. distribute-frac-neg 100.0%

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

   6. distribute-rgt-neg-out 100.0%

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

   7. remove-double-neg 100.0%

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

   8. metadata-eval 100.0%

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

   9. associate-/l* 100.0%

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

   10. fma-define 100.0%

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

   11. neg-mul-1 100.0%

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

   12. *-commutative 100.0%

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

   13. associate-/l* 100.0%

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

   14. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in t around inf 41.8%

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

Developer Target 1: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024186 
(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))