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

Percentage Accurate: 100.0% → 100.0%

Time: 5.3s

Alternatives: 7

Speedup: 0.1×

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. sub-neg 99.7%

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

   2. +-commutative 99.7%

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

   3. associate-+l+ 99.7%

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

   4. associate-/l* 99.9%

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

   5. distribute-frac-neg 99.9%

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

   6. associate-/r/ 100.0%

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

   7. *-commutative 100.0%

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

   8. +-commutative 100.0%

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

   9. fma-def 100.0%

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

   10. neg-mul-1 100.0%

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

   11. associate-/l* 100.0%

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

   12. associate-/r/ 100.0%

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

   13. *-commutative 100.0%

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

   14. metadata-eval 100.0%

       \[\leadsto \mathsf{fma}\left(z, y \cdot \color{blue}{-0.5}, t + \frac{1}{8} \cdot x\right) \]

   15. +-commutative 100.0%

       \[\leadsto \mathsf{fma}\left(z, y \cdot -0.5, \color{blue}{\frac{1}{8} \cdot x + t}\right) \]

   16. fma-def 100.0%

       \[\leadsto \mathsf{fma}\left(z, y \cdot -0.5, \color{blue}{\mathsf{fma}\left(\frac{1}{8}, x, t\right)}\right) \]

   17. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 48.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z \cdot -0.5\right)\\ \mathbf{if}\;t \leq -1.46 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-152}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{+50}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* z -0.5))))
   (if (<= t -1.46e+122)
     t
     (if (<= t -5.7e+79)
       t_1
       (if (<= t -9e+21)
         t
         (if (<= t 2.35e-152)
           (* 0.125 x)
           (if (<= t 2.5e-94)
             t_1
             (if (<= t 3.05e+50) (* 0.125 x) (if (<= t 3.4e+97) t_1 t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z * -0.5);
	double tmp;
	if (t <= -1.46e+122) {
		tmp = t;
	} else if (t <= -5.7e+79) {
		tmp = t_1;
	} else if (t <= -9e+21) {
		tmp = t;
	} else if (t <= 2.35e-152) {
		tmp = 0.125 * x;
	} else if (t <= 2.5e-94) {
		tmp = t_1;
	} else if (t <= 3.05e+50) {
		tmp = 0.125 * x;
	} else if (t <= 3.4e+97) {
		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 = y * (z * (-0.5d0))
    if (t <= (-1.46d+122)) then
        tmp = t
    else if (t <= (-5.7d+79)) then
        tmp = t_1
    else if (t <= (-9d+21)) then
        tmp = t
    else if (t <= 2.35d-152) then
        tmp = 0.125d0 * x
    else if (t <= 2.5d-94) then
        tmp = t_1
    else if (t <= 3.05d+50) then
        tmp = 0.125d0 * x
    else if (t <= 3.4d+97) 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 = y * (z * -0.5);
	double tmp;
	if (t <= -1.46e+122) {
		tmp = t;
	} else if (t <= -5.7e+79) {
		tmp = t_1;
	} else if (t <= -9e+21) {
		tmp = t;
	} else if (t <= 2.35e-152) {
		tmp = 0.125 * x;
	} else if (t <= 2.5e-94) {
		tmp = t_1;
	} else if (t <= 3.05e+50) {
		tmp = 0.125 * x;
	} else if (t <= 3.4e+97) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z * -0.5)
	tmp = 0
	if t <= -1.46e+122:
		tmp = t
	elif t <= -5.7e+79:
		tmp = t_1
	elif t <= -9e+21:
		tmp = t
	elif t <= 2.35e-152:
		tmp = 0.125 * x
	elif t <= 2.5e-94:
		tmp = t_1
	elif t <= 3.05e+50:
		tmp = 0.125 * x
	elif t <= 3.4e+97:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z * -0.5))
	tmp = 0.0
	if (t <= -1.46e+122)
		tmp = t;
	elseif (t <= -5.7e+79)
		tmp = t_1;
	elseif (t <= -9e+21)
		tmp = t;
	elseif (t <= 2.35e-152)
		tmp = Float64(0.125 * x);
	elseif (t <= 2.5e-94)
		tmp = t_1;
	elseif (t <= 3.05e+50)
		tmp = Float64(0.125 * x);
	elseif (t <= 3.4e+97)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z * -0.5);
	tmp = 0.0;
	if (t <= -1.46e+122)
		tmp = t;
	elseif (t <= -5.7e+79)
		tmp = t_1;
	elseif (t <= -9e+21)
		tmp = t;
	elseif (t <= 2.35e-152)
		tmp = 0.125 * x;
	elseif (t <= 2.5e-94)
		tmp = t_1;
	elseif (t <= 3.05e+50)
		tmp = 0.125 * x;
	elseif (t <= 3.4e+97)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z * -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.46e+122], t, If[LessEqual[t, -5.7e+79], t$95$1, If[LessEqual[t, -9e+21], t, If[LessEqual[t, 2.35e-152], N[(0.125 * x), $MachinePrecision], If[LessEqual[t, 2.5e-94], t$95$1, If[LessEqual[t, 3.05e+50], N[(0.125 * x), $MachinePrecision], If[LessEqual[t, 3.4e+97], t$95$1, t]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.46e122 or -5.6999999999999997e79 < t < -9e21 or 3.4000000000000001e97 < t

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 66.8%

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

   if -1.46e122 < t < -5.6999999999999997e79 or 2.35000000000000006e-152 < t < 2.4999999999999998e-94 or 3.05000000000000013e50 < t < 3.4000000000000001e97

   1. Initial program 98.0%

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

      1. metadata-eval 98.0%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 62.4%

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

      1. *-commutative 62.4%

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

      2. associate-*l* 64.4%

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

   7. Simplified 64.4%

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

   if -9e21 < t < 2.35000000000000006e-152 or 2.4999999999999998e-94 < t < 3.05000000000000013e50

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 59.8%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.46 \cdot 10^{+122}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-152}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{+50}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+97}:\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot y \leq -1 \cdot 10^{+102} \lor \neg \left(z \cdot y \leq 2 \cdot 10^{+38}\right):\\ \;\;\;\;t - \left(z \cdot y\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z y) -1e+102) (not (<= (* z y) 2e+38)))
   (- t (* (* z y) 0.5))
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * y) <= -1e+102) || !((z * y) <= 2e+38)) {
		tmp = t - ((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 (((z * y) <= (-1d+102)) .or. (.not. ((z * y) <= 2d+38))) then
        tmp = t - ((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 (((z * y) <= -1e+102) || !((z * y) <= 2e+38)) {
		tmp = t - ((z * y) * 0.5);
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * y) <= -1e+102) or not ((z * y) <= 2e+38):
		tmp = t - ((z * y) * 0.5)
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * y) <= -1e+102) || !(Float64(z * y) <= 2e+38))
		tmp = Float64(t - Float64(Float64(z * 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 (((z * y) <= -1e+102) || ~(((z * y) <= 2e+38)))
		tmp = t - ((z * y) * 0.5);
	else
		tmp = t + (0.125 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * y), $MachinePrecision], -1e+102], N[Not[LessEqual[N[(z * y), $MachinePrecision], 2e+38]], $MachinePrecision]], N[(t - N[(N[(z * y), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -9.99999999999999977e101 or 1.99999999999999995e38 < (*.f64 y z)

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 91.8%

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

   if -9.99999999999999977e101 < (*.f64 y z) < 1.99999999999999995e38

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 92.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -1 \cdot 10^{+102} \lor \neg \left(z \cdot y \leq 2 \cdot 10^{+38}\right):\\ \;\;\;\;t - \left(z \cdot y\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-51} \lor \neg \left(z \leq 1.5 \cdot 10^{+129}\right):\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.25e-51) (not (<= z 1.5e+129)))
   (* y (* z -0.5))
   (+ t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.25e-51) || !(z <= 1.5e+129)) {
		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 ((z <= (-2.25d-51)) .or. (.not. (z <= 1.5d+129))) 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 ((z <= -2.25e-51) || !(z <= 1.5e+129)) {
		tmp = y * (z * -0.5);
	} else {
		tmp = t + (0.125 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.25e-51) or not (z <= 1.5e+129):
		tmp = y * (z * -0.5)
	else:
		tmp = t + (0.125 * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.25e-51) || !(z <= 1.5e+129))
		tmp = Float64(y * Float64(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 ((z <= -2.25e-51) || ~((z <= 1.5e+129)))
		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[z, -2.25e-51], N[Not[LessEqual[z, 1.5e+129]], $MachinePrecision]], N[(y * N[(z * -0.5), $MachinePrecision]), $MachinePrecision], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.24999999999999987e-51 or 1.50000000000000015e129 < z

   1. Initial program 99.1%

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

      1. metadata-eval 99.1%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 64.6%

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

      1. *-commutative 64.6%

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

      2. associate-*l* 65.4%

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

   7. Simplified 65.4%

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

   if -2.24999999999999987e-51 < z < 1.50000000000000015e129

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 83.9%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-51} \lor \neg \left(z \leq 1.5 \cdot 10^{+129}\right):\\ \;\;\;\;y \cdot \left(z \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t + 0.125 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+62}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.75e+22) t (if (<= t 4.8e+62) (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.75e+22) {
		tmp = t;
	} else if (t <= 4.8e+62) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.75d+22)) then
        tmp = t
    else if (t <= 4.8d+62) then
        tmp = 0.125d0 * x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.75e+22) {
		tmp = t;
	} else if (t <= 4.8e+62) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.75e+22:
		tmp = t
	elif t <= 4.8e+62:
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.75e+22)
		tmp = t;
	elseif (t <= 4.8e+62)
		tmp = Float64(0.125 * x);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.75e+22)
		tmp = t;
	elseif (t <= 4.8e+62)
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.75e+22], t, If[LessEqual[t, 4.8e+62], N[(0.125 * x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7500000000000001e22 or 4.8e62 < t

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 60.7%

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

   if -2.7500000000000001e22 < t < 4.8e62

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 54.8%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+62}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t + ((0.125d0 * x) - (y / (2.0d0 / z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. metadata-eval 99.7%

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

   2. associate-/l* 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 7: 32.3% 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 99.7%

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

   1. metadata-eval 99.7%

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

   2. associate-/l* 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in t around inf 31.8%

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

6. Final simplification 31.8%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 100.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024024 
(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))