Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Percentage Accurate: 85.7% → 99.1%

Time: 9.2s

Alternatives: 12

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\frac{y}{a - z}}{\frac{1}{z - t}}\\ t_2 := \left(t - z\right) \cdot y\\ t_3 := \frac{t\_2}{a - z}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+228}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 1.8 \cdot 10^{+282}:\\ \;\;\;\;x - \frac{t\_2}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (/ y (- a z)) (/ 1.0 (- z t)))))
        (t_2 (* (- t z) y))
        (t_3 (/ t_2 (- a z))))
   (if (<= t_3 -1e+228) t_1 (if (<= t_3 1.8e+282) (- x (/ t_2 (- z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / (a - z)) / (1.0 / (z - t)));
	double t_2 = (t - z) * y;
	double t_3 = t_2 / (a - z);
	double tmp;
	if (t_3 <= -1e+228) {
		tmp = t_1;
	} else if (t_3 <= 1.8e+282) {
		tmp = x - (t_2 / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x - ((y / (a - z)) / (1.0d0 / (z - t)))
    t_2 = (t - z) * y
    t_3 = t_2 / (a - z)
    if (t_3 <= (-1d+228)) then
        tmp = t_1
    else if (t_3 <= 1.8d+282) then
        tmp = x - (t_2 / (z - a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / (a - z)) / (1.0 / (z - t)));
	double t_2 = (t - z) * y;
	double t_3 = t_2 / (a - z);
	double tmp;
	if (t_3 <= -1e+228) {
		tmp = t_1;
	} else if (t_3 <= 1.8e+282) {
		tmp = x - (t_2 / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y / (a - z)) / (1.0 / (z - t)))
	t_2 = (t - z) * y
	t_3 = t_2 / (a - z)
	tmp = 0
	if t_3 <= -1e+228:
		tmp = t_1
	elif t_3 <= 1.8e+282:
		tmp = x - (t_2 / (z - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y / Float64(a - z)) / Float64(1.0 / Float64(z - t))))
	t_2 = Float64(Float64(t - z) * y)
	t_3 = Float64(t_2 / Float64(a - z))
	tmp = 0.0
	if (t_3 <= -1e+228)
		tmp = t_1;
	elseif (t_3 <= 1.8e+282)
		tmp = Float64(x - Float64(t_2 / Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y / (a - z)) / (1.0 / (z - t)));
	t_2 = (t - z) * y;
	t_3 = t_2 / (a - z);
	tmp = 0.0;
	if (t_3 <= -1e+228)
		tmp = t_1;
	elseif (t_3 <= 1.8e+282)
		tmp = x - (t_2 / (z - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+228], t$95$1, If[LessEqual[t$95$3, 1.8e+282], N[(x - N[(t$95$2 / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -9.9999999999999992e227 or 1.79999999999999993e282 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 46.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lift--.f64 N/A

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

      6. flip-- N/A

         \[\leadsto x + \color{blue}{\frac{z \cdot z - t \cdot t}{z + t}} \cdot \frac{y}{z - a} \]

      7. clear-num N/A

         \[\leadsto x + \color{blue}{\frac{1}{\frac{z + t}{z \cdot z - t \cdot t}}} \cdot \frac{y}{z - a} \]

      8. associate-*l/ N/A

         \[\leadsto x + \color{blue}{\frac{1 \cdot \frac{y}{z - a}}{\frac{z + t}{z \cdot z - t \cdot t}}} \]

      9. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{1 \cdot \frac{y}{z - a}}{\frac{z + t}{z \cdot z - t \cdot t}}} \]

      10. lower-*.f64 N/A

          \[\leadsto x + \frac{\color{blue}{1 \cdot \frac{y}{z - a}}}{\frac{z + t}{z \cdot z - t \cdot t}} \]

      11. lower-/.f64 N/A

          \[\leadsto x + \frac{1 \cdot \color{blue}{\frac{y}{z - a}}}{\frac{z + t}{z \cdot z - t \cdot t}} \]

      12. clear-num N/A

          \[\leadsto x + \frac{1 \cdot \frac{y}{z - a}}{\color{blue}{\frac{1}{\frac{z \cdot z - t \cdot t}{z + t}}}} \]

      13. flip-- N/A

          \[\leadsto x + \frac{1 \cdot \frac{y}{z - a}}{\frac{1}{\color{blue}{z - t}}} \]

      14. lift--.f64 N/A

          \[\leadsto x + \frac{1 \cdot \frac{y}{z - a}}{\frac{1}{\color{blue}{z - t}}} \]

      15. lower-/.f64 99.8

          \[\leadsto x + \frac{1 \cdot \frac{y}{z - a}}{\color{blue}{\frac{1}{z - t}}} \]

   4. Applied rewrites 99.8%

      \[\leadsto x + \color{blue}{\frac{1 \cdot \frac{y}{z - a}}{\frac{1}{z - t}}} \]

   if -9.9999999999999992e227 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 1.79999999999999993e282

   1. Initial program 99.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq -1 \cdot 10^{+228}:\\ \;\;\;\;x - \frac{\frac{y}{a - z}}{\frac{1}{z - t}}\\ \mathbf{elif}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq 1.8 \cdot 10^{+282}:\\ \;\;\;\;x - \frac{\left(t - z\right) \cdot y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{a - z}}{\frac{1}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - z\right) \cdot y\\ t_2 := \frac{t\_1}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+228}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{elif}\;t\_2 \leq 1.8 \cdot 10^{+282}:\\ \;\;\;\;x - \frac{t\_1}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{a - z}}{\frac{-1}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t z) y)) (t_2 (/ t_1 (- a z))))
   (if (<= t_2 -1e+228)
     (* (/ y (- z a)) (- z t))
     (if (<= t_2 1.8e+282)
       (- x (/ t_1 (- z a)))
       (/ (/ y (- a z)) (/ -1.0 (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) * y;
	double t_2 = t_1 / (a - z);
	double tmp;
	if (t_2 <= -1e+228) {
		tmp = (y / (z - a)) * (z - t);
	} else if (t_2 <= 1.8e+282) {
		tmp = x - (t_1 / (z - a));
	} else {
		tmp = (y / (a - z)) / (-1.0 / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - z) * y
    t_2 = t_1 / (a - z)
    if (t_2 <= (-1d+228)) then
        tmp = (y / (z - a)) * (z - t)
    else if (t_2 <= 1.8d+282) then
        tmp = x - (t_1 / (z - a))
    else
        tmp = (y / (a - z)) / ((-1.0d0) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) * y;
	double t_2 = t_1 / (a - z);
	double tmp;
	if (t_2 <= -1e+228) {
		tmp = (y / (z - a)) * (z - t);
	} else if (t_2 <= 1.8e+282) {
		tmp = x - (t_1 / (z - a));
	} else {
		tmp = (y / (a - z)) / (-1.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - z) * y
	t_2 = t_1 / (a - z)
	tmp = 0
	if t_2 <= -1e+228:
		tmp = (y / (z - a)) * (z - t)
	elif t_2 <= 1.8e+282:
		tmp = x - (t_1 / (z - a))
	else:
		tmp = (y / (a - z)) / (-1.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) * y)
	t_2 = Float64(t_1 / Float64(a - z))
	tmp = 0.0
	if (t_2 <= -1e+228)
		tmp = Float64(Float64(y / Float64(z - a)) * Float64(z - t));
	elseif (t_2 <= 1.8e+282)
		tmp = Float64(x - Float64(t_1 / Float64(z - a)));
	else
		tmp = Float64(Float64(y / Float64(a - z)) / Float64(-1.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - z) * y;
	t_2 = t_1 / (a - z);
	tmp = 0.0;
	if (t_2 <= -1e+228)
		tmp = (y / (z - a)) * (z - t);
	elseif (t_2 <= 1.8e+282)
		tmp = x - (t_1 / (z - a));
	else
		tmp = (y / (a - z)) / (-1.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+228], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1.8e+282], N[(x - N[(t$95$1 / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] / N[(-1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -9.9999999999999992e227

   1. Initial program 51.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{y \cdot \frac{z}{z - a} - y \cdot \frac{t}{z - a}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{\frac{y \cdot z}{z - a}} - y \cdot \frac{t}{z - a} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot y}}{z - a} - y \cdot \frac{t}{z - a} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{y}{z - a}} - y \cdot \frac{t}{z - a} \]

      5. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \color{blue}{\frac{y \cdot t}{z - a}} \]

      6. *-commutative N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \frac{\color{blue}{t \cdot y}}{z - a} \]

      7. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \color{blue}{t \cdot \frac{y}{z - a}} \]

      8. distribute-rgt-out-- N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 91.6

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

   5. Applied rewrites 91.6%

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

   if -9.9999999999999992e227 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 1.79999999999999993e282

   1. Initial program 99.4%

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

   if 1.79999999999999993e282 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 39.2%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{y \cdot \frac{z}{z - a} - y \cdot \frac{t}{z - a}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{\frac{y \cdot z}{z - a}} - y \cdot \frac{t}{z - a} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot y}}{z - a} - y \cdot \frac{t}{z - a} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{y}{z - a}} - y \cdot \frac{t}{z - a} \]

      5. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \color{blue}{\frac{y \cdot t}{z - a}} \]

      6. *-commutative N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \frac{\color{blue}{t \cdot y}}{z - a} \]

      7. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \color{blue}{t \cdot \frac{y}{z - a}} \]

      8. distribute-rgt-out-- N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 89.6

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

   5. Applied rewrites 89.6%

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

   7. Applied rewrites 89.8%

      \[\leadsto \frac{\frac{-y}{z - a}}{\color{blue}{\frac{-1}{z - t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq -1 \cdot 10^{+228}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq 1.8 \cdot 10^{+282}:\\ \;\;\;\;x - \frac{\left(t - z\right) \cdot y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{a - z}}{\frac{-1}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a} \cdot \left(z - t\right)\\ t_2 := \left(t - z\right) \cdot y\\ t_3 := \frac{t\_2}{a - z}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+228}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 10^{+293}:\\ \;\;\;\;x - \frac{t\_2}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- z a)) (- z t)))
        (t_2 (* (- t z) y))
        (t_3 (/ t_2 (- a z))))
   (if (<= t_3 -1e+228) t_1 (if (<= t_3 1e+293) (- x (/ t_2 (- z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * (z - t);
	double t_2 = (t - z) * y;
	double t_3 = t_2 / (a - z);
	double tmp;
	if (t_3 <= -1e+228) {
		tmp = t_1;
	} else if (t_3 <= 1e+293) {
		tmp = x - (t_2 / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y / (z - a)) * (z - t)
    t_2 = (t - z) * y
    t_3 = t_2 / (a - z)
    if (t_3 <= (-1d+228)) then
        tmp = t_1
    else if (t_3 <= 1d+293) then
        tmp = x - (t_2 / (z - a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * (z - t);
	double t_2 = (t - z) * y;
	double t_3 = t_2 / (a - z);
	double tmp;
	if (t_3 <= -1e+228) {
		tmp = t_1;
	} else if (t_3 <= 1e+293) {
		tmp = x - (t_2 / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (z - a)) * (z - t)
	t_2 = (t - z) * y
	t_3 = t_2 / (a - z)
	tmp = 0
	if t_3 <= -1e+228:
		tmp = t_1
	elif t_3 <= 1e+293:
		tmp = x - (t_2 / (z - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(z - a)) * Float64(z - t))
	t_2 = Float64(Float64(t - z) * y)
	t_3 = Float64(t_2 / Float64(a - z))
	tmp = 0.0
	if (t_3 <= -1e+228)
		tmp = t_1;
	elseif (t_3 <= 1e+293)
		tmp = Float64(x - Float64(t_2 / Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (z - a)) * (z - t);
	t_2 = (t - z) * y;
	t_3 = t_2 / (a - z);
	tmp = 0.0;
	if (t_3 <= -1e+228)
		tmp = t_1;
	elseif (t_3 <= 1e+293)
		tmp = x - (t_2 / (z - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+228], t$95$1, If[LessEqual[t$95$3, 1e+293], N[(x - N[(t$95$2 / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -9.9999999999999992e227 or 9.9999999999999992e292 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 44.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{y \cdot \frac{z}{z - a} - y \cdot \frac{t}{z - a}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{\frac{y \cdot z}{z - a}} - y \cdot \frac{t}{z - a} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot y}}{z - a} - y \cdot \frac{t}{z - a} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{y}{z - a}} - y \cdot \frac{t}{z - a} \]

      5. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \color{blue}{\frac{y \cdot t}{z - a}} \]

      6. *-commutative N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \frac{\color{blue}{t \cdot y}}{z - a} \]

      7. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \color{blue}{t \cdot \frac{y}{z - a}} \]

      8. distribute-rgt-out-- N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 90.6

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

   5. Applied rewrites 90.6%

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

   if -9.9999999999999992e227 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 9.9999999999999992e292

   1. Initial program 99.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq -1 \cdot 10^{+228}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq 10^{+293}:\\ \;\;\;\;x - \frac{\left(t - z\right) \cdot y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a} \cdot \left(z - t\right)\\ t_2 := \frac{\left(t - z\right) \cdot y}{a - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+121}:\\ \;\;\;\;x - \frac{z \cdot y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- z a)) (- z t))) (t_2 (/ (* (- t z) y) (- a z))))
   (if (<= t_2 -2e+111)
     t_1
     (if (<= t_2 5e+121) (- x (/ (* z y) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * (z - t);
	double t_2 = ((t - z) * y) / (a - z);
	double tmp;
	if (t_2 <= -2e+111) {
		tmp = t_1;
	} else if (t_2 <= 5e+121) {
		tmp = x - ((z * y) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y / (z - a)) * (z - t)
    t_2 = ((t - z) * y) / (a - z)
    if (t_2 <= (-2d+111)) then
        tmp = t_1
    else if (t_2 <= 5d+121) then
        tmp = x - ((z * y) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * (z - t);
	double t_2 = ((t - z) * y) / (a - z);
	double tmp;
	if (t_2 <= -2e+111) {
		tmp = t_1;
	} else if (t_2 <= 5e+121) {
		tmp = x - ((z * y) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (z - a)) * (z - t)
	t_2 = ((t - z) * y) / (a - z)
	tmp = 0
	if t_2 <= -2e+111:
		tmp = t_1
	elif t_2 <= 5e+121:
		tmp = x - ((z * y) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(z - a)) * Float64(z - t))
	t_2 = Float64(Float64(Float64(t - z) * y) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= -2e+111)
		tmp = t_1;
	elseif (t_2 <= 5e+121)
		tmp = Float64(x - Float64(Float64(z * y) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (z - a)) * (z - t);
	t_2 = ((t - z) * y) / (a - z);
	tmp = 0.0;
	if (t_2 <= -2e+111)
		tmp = t_1;
	elseif (t_2 <= 5e+121)
		tmp = x - ((z * y) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+111], t$95$1, If[LessEqual[t$95$2, 5e+121], N[(x - N[(N[(z * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -1.99999999999999991e111 or 5.00000000000000007e121 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 62.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{y \cdot \frac{z}{z - a} - y \cdot \frac{t}{z - a}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{\frac{y \cdot z}{z - a}} - y \cdot \frac{t}{z - a} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot y}}{z - a} - y \cdot \frac{t}{z - a} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{y}{z - a}} - y \cdot \frac{t}{z - a} \]

      5. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \color{blue}{\frac{y \cdot t}{z - a}} \]

      6. *-commutative N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \frac{\color{blue}{t \cdot y}}{z - a} \]

      7. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \color{blue}{t \cdot \frac{y}{z - a}} \]

      8. distribute-rgt-out-- N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 84.9

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

   5. Applied rewrites 84.9%

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

   if -1.99999999999999991e111 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 5.00000000000000007e121

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0

      \[\leadsto x + \frac{\color{blue}{y \cdot z}}{z - a} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x + \frac{\color{blue}{z \cdot y}}{z - a} \]

      2. lower-*.f64 89.9

         \[\leadsto x + \frac{\color{blue}{z \cdot y}}{z - a} \]

   5. Applied rewrites 89.9%

      \[\leadsto x + \frac{\color{blue}{z \cdot y}}{z - a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq -2 \cdot 10^{+111}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq 5 \cdot 10^{+121}:\\ \;\;\;\;x - \frac{z \cdot y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a} \cdot \left(z - t\right)\\ t_2 := \frac{\left(t - z\right) \cdot y}{a - z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+121}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- z a)) (- z t))) (t_2 (/ (* (- t z) y) (- a z))))
   (if (<= t_2 -2e+111) t_1 (if (<= t_2 5e+121) (fma (/ z (- z a)) y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * (z - t);
	double t_2 = ((t - z) * y) / (a - z);
	double tmp;
	if (t_2 <= -2e+111) {
		tmp = t_1;
	} else if (t_2 <= 5e+121) {
		tmp = fma((z / (z - a)), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(z - a)) * Float64(z - t))
	t_2 = Float64(Float64(Float64(t - z) * y) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= -2e+111)
		tmp = t_1;
	elseif (t_2 <= 5e+121)
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+111], t$95$1, If[LessEqual[t$95$2, 5e+121], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -1.99999999999999991e111 or 5.00000000000000007e121 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 62.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{y \cdot \frac{z}{z - a} - y \cdot \frac{t}{z - a}} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{\frac{y \cdot z}{z - a}} - y \cdot \frac{t}{z - a} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot y}}{z - a} - y \cdot \frac{t}{z - a} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{y}{z - a}} - y \cdot \frac{t}{z - a} \]

      5. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \color{blue}{\frac{y \cdot t}{z - a}} \]

      6. *-commutative N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \frac{\color{blue}{t \cdot y}}{z - a} \]

      7. associate-/l* N/A

         \[\leadsto z \cdot \frac{y}{z - a} - \color{blue}{t \cdot \frac{y}{z - a}} \]

      8. distribute-rgt-out-- N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 84.9

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

   5. Applied rewrites 84.9%

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

   if -1.99999999999999991e111 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 5.00000000000000007e121

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{z - a}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot z}{z - a} + x} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{z}{z - a}} + x \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\frac{z}{z - a} \cdot y} + x \]

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 89.5

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

   5. Applied rewrites 89.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq -2 \cdot 10^{+111}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{\left(t - z\right) \cdot y}{a - z} \leq 5 \cdot 10^{+121}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.28 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-t}{z}, y, x\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-66}:\\ \;\;\;\;\frac{t \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma z (/ y (- z a)) x)))
   (if (<= z -1.25e+26)
     t_1
     (if (<= z -1.28e-79)
       (fma (/ (- t) z) y x)
       (if (<= z 1.3e-66) (+ (/ (* t y) a) x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(z, (y / (z - a)), x);
	double tmp;
	if (z <= -1.25e+26) {
		tmp = t_1;
	} else if (z <= -1.28e-79) {
		tmp = fma((-t / z), y, x);
	} else if (z <= 1.3e-66) {
		tmp = ((t * y) / a) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(z, Float64(y / Float64(z - a)), x)
	tmp = 0.0
	if (z <= -1.25e+26)
		tmp = t_1;
	elseif (z <= -1.28e-79)
		tmp = fma(Float64(Float64(-t) / z), y, x);
	elseif (z <= 1.3e-66)
		tmp = Float64(Float64(Float64(t * y) / a) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.25e+26], t$95$1, If[LessEqual[z, -1.28e-79], N[(N[((-t) / z), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[z, 1.3e-66], N[(N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25e26 or 1.2999999999999999e-66 < z

   1. Initial program 74.8%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{z - a}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot z}{z - a} + x} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{z}{z - a}} + x \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\frac{z}{z - a} \cdot y} + x \]

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 85.2

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

   5. Applied rewrites 85.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 82.2%

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

   if -1.25e26 < z < -1.28e-79

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(z - t\right)}{z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{z}} + x \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\frac{z - t}{z} \cdot y} + x \]

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 94.7

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

   5. Applied rewrites 94.7%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\frac{-1 \cdot t}{z}, y, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 83.9%

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

   if -1.28e-79 < z < 1.2999999999999999e-66

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]

      2. lower-*.f64 88.2

         \[\leadsto x + \frac{\color{blue}{t \cdot y}}{a} \]

   5. Applied rewrites 88.2%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \mathbf{elif}\;z \leq -1.28 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-t}{z}, y, x\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-66}:\\ \;\;\;\;\frac{t \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.28 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-t}{z}, y, x\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+27)
   (+ x y)
   (if (<= z -1.28e-79)
     (fma (/ (- t) z) y x)
     (if (<= z 2.25e-26) (+ (* (/ t a) y) x) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+27) {
		tmp = x + y;
	} else if (z <= -1.28e-79) {
		tmp = fma((-t / z), y, x);
	} else if (z <= 2.25e-26) {
		tmp = ((t / a) * y) + x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+27)
		tmp = Float64(x + y);
	elseif (z <= -1.28e-79)
		tmp = fma(Float64(Float64(-t) / z), y, x);
	elseif (z <= 2.25e-26)
		tmp = Float64(Float64(Float64(t / a) * y) + x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+27], N[(x + y), $MachinePrecision], If[LessEqual[z, -1.28e-79], N[(N[((-t) / z), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[z, 2.25e-26], N[(N[(N[(t / a), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999995e27 or 2.2499999999999999e-26 < z

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{y + x} \]

      2. lower-+.f64 74.4

         \[\leadsto \color{blue}{y + x} \]

   5. Applied rewrites 74.4%

      \[\leadsto \color{blue}{y + x} \]

   if -1.24999999999999995e27 < z < -1.28e-79

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(z - t\right)}{z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{z}} + x \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\frac{z - t}{z} \cdot y} + x \]

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 94.7

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

   5. Applied rewrites 94.7%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\frac{-1 \cdot t}{z}, y, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 83.9%

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

   if -1.28e-79 < z < 2.2499999999999999e-26

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]

      2. lower-*.f64 84.1

         \[\leadsto x + \frac{\color{blue}{t \cdot y}}{a} \]

   5. Applied rewrites 84.1%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

   7. Applied rewrites 84.8%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -1.28 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-t}{z}, y, x\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-77}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-t}{z}, y, x\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+27)
   (+ x y)
   (if (<= z -4.8e-77)
     (fma (/ (- t) z) y x)
     (if (<= z 2.25e-26) (fma (/ y a) t x) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+27) {
		tmp = x + y;
	} else if (z <= -4.8e-77) {
		tmp = fma((-t / z), y, x);
	} else if (z <= 2.25e-26) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+27)
		tmp = Float64(x + y);
	elseif (z <= -4.8e-77)
		tmp = fma(Float64(Float64(-t) / z), y, x);
	elseif (z <= 2.25e-26)
		tmp = fma(Float64(y / a), t, x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+27], N[(x + y), $MachinePrecision], If[LessEqual[z, -4.8e-77], N[(N[((-t) / z), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[z, 2.25e-26], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999995e27 or 2.2499999999999999e-26 < z

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{y + x} \]

      2. lower-+.f64 74.4

         \[\leadsto \color{blue}{y + x} \]

   5. Applied rewrites 74.4%

      \[\leadsto \color{blue}{y + x} \]

   if -1.24999999999999995e27 < z < -4.7999999999999998e-77

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(z - t\right)}{z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{z}} + x \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\frac{z - t}{z} \cdot y} + x \]

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 94.7

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

   5. Applied rewrites 94.7%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\frac{-1 \cdot t}{z}, y, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 83.9%

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

   if -4.7999999999999998e-77 < z < 2.2499999999999999e-26

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{t \cdot y}{a} + x} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} + x \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{a} \cdot t} + x \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, t, x\right)} \]

      5. lower-/.f64 84.2

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, t, x\right) \]

   5. Applied rewrites 84.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, t, x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-77}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-t}{z}, y, x\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.8e+16)
   (fma (/ z (- z a)) y x)
   (if (<= a 4.2e-32) (fma (/ (- z t) z) y x) (+ (* (/ t a) y) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e+16) {
		tmp = fma((z / (z - a)), y, x);
	} else if (a <= 4.2e-32) {
		tmp = fma(((z - t) / z), y, x);
	} else {
		tmp = ((t / a) * y) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.8e+16)
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	elseif (a <= 4.2e-32)
		tmp = fma(Float64(Float64(z - t) / z), y, x);
	else
		tmp = Float64(Float64(Float64(t / a) * y) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.8e+16], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[a, 4.2e-32], N[(N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(N[(t / a), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.8e16

   1. Initial program 78.8%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{z - a}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot z}{z - a} + x} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{z}{z - a}} + x \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\frac{z}{z - a} \cdot y} + x \]

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 88.1

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

   5. Applied rewrites 88.1%

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

   if -2.8e16 < a < 4.1999999999999998e-32

   1. Initial program 88.6%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(z - t\right)}{z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{z}} + x \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\frac{z - t}{z} \cdot y} + x \]

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 85.8

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

   5. Applied rewrites 85.8%

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

   if 4.1999999999999998e-32 < a

   1. Initial program 83.5%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]

      2. lower-*.f64 77.5

         \[\leadsto x + \frac{\color{blue}{t \cdot y}}{a} \]

   5. Applied rewrites 77.5%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

   7. Applied rewrites 84.5%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-32}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{t \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ z (- z a)) y x)))
   (if (<= z -9.5e-82) t_1 (if (<= z 7.6e-64) (+ (/ (* t y) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((z / (z - a)), y, x);
	double tmp;
	if (z <= -9.5e-82) {
		tmp = t_1;
	} else if (z <= 7.6e-64) {
		tmp = ((t * y) / a) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(z / Float64(z - a)), y, x)
	tmp = 0.0
	if (z <= -9.5e-82)
		tmp = t_1;
	elseif (z <= 7.6e-64)
		tmp = Float64(Float64(Float64(t * y) / a) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -9.5e-82], t$95$1, If[LessEqual[z, 7.6e-64], N[(N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999996e-82 or 7.6000000000000003e-64 < z

   1. Initial program 77.6%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{z - a}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot z}{z - a} + x} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{z}{z - a}} + x \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\frac{z}{z - a} \cdot y} + x \]

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 82.7

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

   5. Applied rewrites 82.7%

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

   if -9.4999999999999996e-82 < z < 7.6000000000000003e-64

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{t \cdot y}{a}} \]

      2. lower-*.f64 88.2

         \[\leadsto x + \frac{\color{blue}{t \cdot y}}{a} \]

   5. Applied rewrites 88.2%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-82}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-64}:\\ \;\;\;\;\frac{t \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.1e-5) (+ x y) (if (<= z 2.25e-26) (fma (/ y a) t x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e-5) {
		tmp = x + y;
	} else if (z <= 2.25e-26) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.1e-5)
		tmp = Float64(x + y);
	elseif (z <= 2.25e-26)
		tmp = fma(Float64(y / a), t, x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.1e-5], N[(x + y), $MachinePrecision], If[LessEqual[z, 2.25e-26], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.09999999999999988e-5 or 2.2499999999999999e-26 < z

   1. Initial program 74.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{y + x} \]

      2. lower-+.f64 73.0

         \[\leadsto \color{blue}{y + x} \]

   5. Applied rewrites 73.0%

      \[\leadsto \color{blue}{y + x} \]

   if -2.09999999999999988e-5 < z < 2.2499999999999999e-26

   1. Initial program 96.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{t \cdot y}{a} + x} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{t \cdot \frac{y}{a}} + x \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{a} \cdot t} + x \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, t, x\right)} \]

      5. lower-/.f64 83.0

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, t, x\right) \]

   5. Applied rewrites 83.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, t, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-5}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.6% accurate, 6.5× speedup

Math

\[\begin{array}{l} \\ x + y \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x y))

C

double code(double x, double y, double z, double t, double a) {
	return x + y;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + y
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + y;
}

Python

def code(x, y, z, t, a):
	return x + y

Julia

function code(x, y, z, t, a)
	return Float64(x + y)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + y;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 84.8%

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

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{x + y} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{y + x} \]

   2. lower-+.f64 61.2

      \[\leadsto \color{blue}{y + x} \]

5. Applied rewrites 61.2%

   \[\leadsto \color{blue}{y + x} \]

6. Final simplification 61.2%

   \[\leadsto x + y \]
7. Add Preprocessing

Developer Target 1: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{z - a}{z - t}} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ y (/ (- z a) (- z t)))))

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y / ((z - a) / (z - t)))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x + (y / ((z - a) / (z - t)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y / Float64(Float64(z - a) / Float64(z - t))))
end

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024243 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- z a) (- z t)))))

  (+ x (/ (* y (- z t)) (- z a))))