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

Percentage Accurate: 85.4% → 99.5%

Time: 8.5s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+301} \lor \neg \left(t_1 \leq 4 \cdot 10^{+258}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- a t))))
   (if (or (<= t_1 -2e+301) (not (<= t_1 4e+258)))
     (+ x (/ (- z t) (/ (- a t) y)))
     (+ x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if ((t_1 <= -2e+301) || !(t_1 <= 4e+258)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = x + 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) :: tmp
    t_1 = (y * (z - t)) / (a - t)
    if ((t_1 <= (-2d+301)) .or. (.not. (t_1 <= 4d+258))) then
        tmp = x + ((z - t) / ((a - t) / y))
    else
        tmp = x + 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 - t)) / (a - t);
	double tmp;
	if ((t_1 <= -2e+301) || !(t_1 <= 4e+258)) {
		tmp = x + ((z - t) / ((a - t) / y));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (a - t)
	tmp = 0
	if (t_1 <= -2e+301) or not (t_1 <= 4e+258):
		tmp = x + ((z - t) / ((a - t) / y))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(a - t))
	tmp = 0.0
	if ((t_1 <= -2e+301) || !(t_1 <= 4e+258))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(Float64(a - t) / y)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (a - t);
	tmp = 0.0;
	if ((t_1 <= -2e+301) || ~((t_1 <= 4e+258)))
		tmp = x + ((z - t) / ((a - t) / y));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+301], N[Not[LessEqual[t$95$1, 4e+258]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -2.00000000000000011e301 or 4.00000000000000023e258 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 30.3%

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

      1. *-commutative 30.3%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -2.00000000000000011e301 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 4.00000000000000023e258

   1. Initial program 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{+301} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \leq 4 \cdot 10^{+258}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \]

Alternative 2: 93.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+290}\right):\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- a t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+290)))
     (+ x (/ (- t z) (/ t y)))
     (+ x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+290)) {
		tmp = x + ((t - z) / (t / y));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+290)) {
		tmp = x + ((t - z) / (t / y));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (a - t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+290):
		tmp = x + ((t - z) / (t / y))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(a - t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+290))
		tmp = Float64(x + Float64(Float64(t - z) / Float64(t / y)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (a - t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+290)))
		tmp = x + ((t - z) / (t / y));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+290]], $MachinePrecision]], N[(x + N[(N[(t - z), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -inf.0 or 1.00000000000000006e290 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 28.5%

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

   2. Taylor expanded in a around 0 26.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(z - t\right)}{t} + x} \]
   3. Step-by-step derivation

      1. +-commutative 26.3%

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

      2. mul-1-neg 26.3%

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

      3. *-commutative 26.3%

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

      4. unsub-neg 26.3%

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

      5. associate-/l* 77.3%

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

   4. Simplified 77.3%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 1.00000000000000006e290

   1. Initial program 99.8%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \leq 10^{+290}\right):\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \]

Alternative 3: 86.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 6400000000:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{y}}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.8e+59)
   (+ x (/ (- t z) (/ t y)))
   (if (<= t 6400000000.0)
     (+ x (/ 1.0 (/ (/ (- a t) y) z)))
     (- x (/ y (/ (- a t) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.8e+59) {
		tmp = x + ((t - z) / (t / y));
	} else if (t <= 6400000000.0) {
		tmp = x + (1.0 / (((a - t) / y) / z));
	} else {
		tmp = x - (y / ((a - t) / 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) :: tmp
    if (t <= (-4.8d+59)) then
        tmp = x + ((t - z) / (t / y))
    else if (t <= 6400000000.0d0) then
        tmp = x + (1.0d0 / (((a - t) / y) / z))
    else
        tmp = x - (y / ((a - t) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.8e+59) {
		tmp = x + ((t - z) / (t / y));
	} else if (t <= 6400000000.0) {
		tmp = x + (1.0 / (((a - t) / y) / z));
	} else {
		tmp = x - (y / ((a - t) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.8e+59:
		tmp = x + ((t - z) / (t / y))
	elif t <= 6400000000.0:
		tmp = x + (1.0 / (((a - t) / y) / z))
	else:
		tmp = x - (y / ((a - t) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.8e+59)
		tmp = Float64(x + Float64(Float64(t - z) / Float64(t / y)));
	elseif (t <= 6400000000.0)
		tmp = Float64(x + Float64(1.0 / Float64(Float64(Float64(a - t) / y) / z)));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(a - t) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.8e+59)
		tmp = x + ((t - z) / (t / y));
	elseif (t <= 6400000000.0)
		tmp = x + (1.0 / (((a - t) / y) / z));
	else
		tmp = x - (y / ((a - t) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.8e+59], N[(x + N[(N[(t - z), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6400000000.0], N[(x + N[(1.0 / N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.8000000000000004e59

   1. Initial program 71.2%

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

   2. Taylor expanded in a around 0 68.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(z - t\right)}{t} + x} \]
   3. Step-by-step derivation

      1. +-commutative 68.9%

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

      2. mul-1-neg 68.9%

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

      3. *-commutative 68.9%

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

      4. unsub-neg 68.9%

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

      5. associate-/l* 86.4%

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

   4. Simplified 86.4%

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

   if -4.8000000000000004e59 < t < 6.4e9

   1. Initial program 93.4%

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

      1. clear-num 93.4%

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

      2. inv-pow 93.4%

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

   3. Applied egg-rr 93.4%

      \[\leadsto x + \color{blue}{{\left(\frac{a - t}{y \cdot \left(z - t\right)}\right)}^{-1}} \]
   4. Step-by-step derivation

      1. unpow-1 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in z around inf 86.3%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{a - t}{y \cdot z}}} \]
   7. Step-by-step derivation

      1. associate-/r* 90.8%

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

   8. Simplified 90.8%

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

   if 6.4e9 < t

   1. Initial program 57.8%

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

   2. Taylor expanded in z around 0 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. *-commutative 54.8%

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

      4. associate-*l/ 92.9%

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

      5. unsub-neg 92.9%

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

      6. associate-*l/ 54.8%

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

      7. *-commutative 54.8%

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

      8. associate-/l* 92.9%

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

   4. Simplified 92.9%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 6400000000:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{y}}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{t}}\\ \end{array} \]

Alternative 4: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+119} \lor \neg \left(t \leq 15000000000\right):\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9e+119) (not (<= t 15000000000.0)))
   (- x (* y (/ t (- a t))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9e+119) || !(t <= 15000000000.0)) {
		tmp = x - (y * (t / (a - t)));
	} else {
		tmp = x + (z * (y / (a - 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) :: tmp
    if ((t <= (-9d+119)) .or. (.not. (t <= 15000000000.0d0))) then
        tmp = x - (y * (t / (a - t)))
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9e+119) || !(t <= 15000000000.0)) {
		tmp = x - (y * (t / (a - t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9e+119) or not (t <= 15000000000.0):
		tmp = x - (y * (t / (a - t)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9e+119) || !(t <= 15000000000.0))
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9e+119) || ~((t <= 15000000000.0)))
		tmp = x - (y * (t / (a - t)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9e+119], N[Not[LessEqual[t, 15000000000.0]], $MachinePrecision]], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.00000000000000039e119 or 1.5e10 < t

   1. Initial program 61.4%

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

      1. +-commutative 61.4%

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

      2. associate-*l/ 95.6%

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

      3. fma-def 95.6%

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

   3. Simplified 95.6%

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

      1. fma-udef 95.6%

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

      2. associate-*l/ 61.4%

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

      3. associate-/l* 99.9%

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

      4. div-inv 99.9%

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

      5. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around 0 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. associate-*r/ 91.4%

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

      4. unsub-neg 91.4%

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

   8. Simplified 91.4%

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

   if -9.00000000000000039e119 < t < 1.5e10

   1. Initial program 93.2%

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

   2. Taylor expanded in z around inf 84.7%

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

      1. associate-*l/ 89.6%

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

      2. *-commutative 89.6%

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

   4. Simplified 89.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+119} \lor \neg \left(t \leq 15000000000\right):\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 5: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+112}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+115}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.6e+112)
   (+ y x)
   (if (<= t 3e+115) (+ x (* z (/ y (- a t)))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e+112) {
		tmp = y + x;
	} else if (t <= 3e+115) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = y + x;
	}
	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) :: tmp
    if (t <= (-1.6d+112)) then
        tmp = y + x
    else if (t <= 3d+115) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e+112) {
		tmp = y + x;
	} else if (t <= 3e+115) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.6e+112:
		tmp = y + x
	elif t <= 3e+115:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.6e+112)
		tmp = Float64(y + x);
	elseif (t <= 3e+115)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.6e+112)
		tmp = y + x;
	elseif (t <= 3e+115)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.6e+112], N[(y + x), $MachinePrecision], If[LessEqual[t, 3e+115], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.59999999999999993e112 or 3e115 < t

   1. Initial program 54.5%

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

   2. Taylor expanded in t around inf 88.4%

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

   if -1.59999999999999993e112 < t < 3e115

   1. Initial program 92.9%

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

   2. Taylor expanded in z around inf 83.4%

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

      1. associate-*l/ 88.2%

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

      2. *-commutative 88.2%

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

   4. Simplified 88.2%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+112}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+115}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+112}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{elif}\;t \leq 2500000000000:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.6e+112)
   (- x (* y (/ t (- a t))))
   (if (<= t 2500000000000.0)
     (+ x (* z (/ y (- a t))))
     (- x (/ y (/ (- a t) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e+112) {
		tmp = x - (y * (t / (a - t)));
	} else if (t <= 2500000000000.0) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a - t) / 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) :: tmp
    if (t <= (-1.6d+112)) then
        tmp = x - (y * (t / (a - t)))
    else if (t <= 2500000000000.0d0) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (y / ((a - t) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e+112) {
		tmp = x - (y * (t / (a - t)));
	} else if (t <= 2500000000000.0) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a - t) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.6e+112:
		tmp = x - (y * (t / (a - t)))
	elif t <= 2500000000000.0:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (y / ((a - t) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.6e+112)
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	elseif (t <= 2500000000000.0)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(a - t) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.6e+112)
		tmp = x - (y * (t / (a - t)));
	elseif (t <= 2500000000000.0)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (y / ((a - t) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.6e+112], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2500000000000.0], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.59999999999999993e112

   1. Initial program 67.1%

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

      1. +-commutative 67.1%

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

      2. associate-*l/ 91.7%

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

      3. fma-def 91.7%

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

   3. Simplified 91.7%

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

      1. fma-udef 91.7%

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

      2. associate-*l/ 67.1%

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

      3. associate-/l* 99.9%

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

      4. div-inv 99.9%

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

      5. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around 0 60.2%

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

      1. +-commutative 60.2%

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

      2. mul-1-neg 60.2%

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

      3. associate-*r/ 89.0%

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

      4. unsub-neg 89.0%

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

   8. Simplified 89.0%

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

   if -1.59999999999999993e112 < t < 2.5e12

   1. Initial program 93.2%

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

   2. Taylor expanded in z around inf 84.7%

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

      1. associate-*l/ 89.6%

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

      2. *-commutative 89.6%

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

   4. Simplified 89.6%

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

   if 2.5e12 < t

   1. Initial program 57.8%

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

   2. Taylor expanded in z around 0 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. *-commutative 54.8%

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

      4. associate-*l/ 92.9%

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

      5. unsub-neg 92.9%

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

      6. associate-*l/ 54.8%

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

      7. *-commutative 54.8%

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

      8. associate-/l* 92.9%

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

   4. Simplified 92.9%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+112}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{elif}\;t \leq 2500000000000:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{t}}\\ \end{array} \]

Alternative 7: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.6e+59)
   (+ x (/ (- t z) (/ t y)))
   (if (<= t 7e+14) (+ x (* z (/ y (- a t)))) (- x (/ y (/ (- a t) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.6e+59) {
		tmp = x + ((t - z) / (t / y));
	} else if (t <= 7e+14) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a - t) / 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) :: tmp
    if (t <= (-5.6d+59)) then
        tmp = x + ((t - z) / (t / y))
    else if (t <= 7d+14) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (y / ((a - t) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.6e+59) {
		tmp = x + ((t - z) / (t / y));
	} else if (t <= 7e+14) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a - t) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.6e+59:
		tmp = x + ((t - z) / (t / y))
	elif t <= 7e+14:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (y / ((a - t) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.6e+59)
		tmp = Float64(x + Float64(Float64(t - z) / Float64(t / y)));
	elseif (t <= 7e+14)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(a - t) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.6e+59)
		tmp = x + ((t - z) / (t / y));
	elseif (t <= 7e+14)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (y / ((a - t) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.6e+59], N[(x + N[(N[(t - z), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+14], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5999999999999996e59

   1. Initial program 71.2%

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

   2. Taylor expanded in a around 0 68.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(z - t\right)}{t} + x} \]
   3. Step-by-step derivation

      1. +-commutative 68.9%

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

      2. mul-1-neg 68.9%

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

      3. *-commutative 68.9%

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

      4. unsub-neg 68.9%

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

      5. associate-/l* 86.4%

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

   4. Simplified 86.4%

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

   if -5.5999999999999996e59 < t < 7e14

   1. Initial program 93.4%

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

   2. Taylor expanded in z around inf 86.3%

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

      1. associate-*l/ 90.8%

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

      2. *-commutative 90.8%

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

   4. Simplified 90.8%

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

   if 7e14 < t

   1. Initial program 57.8%

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

   2. Taylor expanded in z around 0 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. *-commutative 54.8%

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

      4. associate-*l/ 92.9%

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

      5. unsub-neg 92.9%

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

      6. associate-*l/ 54.8%

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

      7. *-commutative 54.8%

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

      8. associate-/l* 92.9%

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

   4. Simplified 92.9%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+14}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{t}}\\ \end{array} \]

Alternative 8: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+20}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-14}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2e+20) (+ y x) (if (<= t 6.6e-14) (+ x (* z (/ y a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2e+20) {
		tmp = y + x;
	} else if (t <= 6.6e-14) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y + x;
	}
	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) :: tmp
    if (t <= (-2d+20)) then
        tmp = y + x
    else if (t <= 6.6d-14) then
        tmp = x + (z * (y / a))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2e+20) {
		tmp = y + x;
	} else if (t <= 6.6e-14) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2e+20:
		tmp = y + x
	elif t <= 6.6e-14:
		tmp = x + (z * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2e+20)
		tmp = Float64(y + x);
	elseif (t <= 6.6e-14)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2e+20)
		tmp = y + x;
	elseif (t <= 6.6e-14)
		tmp = x + (z * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2e+20], N[(y + x), $MachinePrecision], If[LessEqual[t, 6.6e-14], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2e20 or 6.5999999999999996e-14 < t

   1. Initial program 66.2%

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

   2. Taylor expanded in t around inf 80.4%

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

   if -2e20 < t < 6.5999999999999996e-14

   1. Initial program 94.2%

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

   2. Taylor expanded in z around inf 87.9%

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

      1. associate-*l/ 92.2%

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

      2. *-commutative 92.2%

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

   4. Simplified 92.2%

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

   5. Taylor expanded in a around inf 83.7%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+20}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-14}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = (y * ((z - t) / (a - t))) + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.7%

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

   1. +-commutative 78.7%

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

   2. associate-*l/ 96.0%

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

   3. fma-def 96.0%

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

3. Simplified 96.0%

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

   1. fma-udef 96.0%

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

   2. associate-*l/ 78.7%

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

   3. associate-/l* 98.7%

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

   4. div-inv 98.7%

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

   5. clear-num 98.8%

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

5. Applied egg-rr 98.8%

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

6. Final simplification 98.8%

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

Alternative 10: 63.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-161}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.3e-161) (+ y x) (if (<= t 8.4e-19) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e-161) {
		tmp = y + x;
	} else if (t <= 8.4e-19) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	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) :: tmp
    if (t <= (-1.3d-161)) then
        tmp = y + x
    else if (t <= 8.4d-19) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e-161) {
		tmp = y + x;
	} else if (t <= 8.4e-19) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.3e-161:
		tmp = y + x
	elif t <= 8.4e-19:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.3e-161)
		tmp = Float64(y + x);
	elseif (t <= 8.4e-19)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.3e-161)
		tmp = y + x;
	elseif (t <= 8.4e-19)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.3e-161], N[(y + x), $MachinePrecision], If[LessEqual[t, 8.4e-19], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.29999999999999998e-161 or 8.3999999999999996e-19 < t

   1. Initial program 69.9%

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

   2. Taylor expanded in t around inf 76.1%

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

   if -1.29999999999999998e-161 < t < 8.3999999999999996e-19

   1. Initial program 95.6%

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

   2. Taylor expanded in x around inf 56.6%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-161}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 11: 51.5% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 78.7%

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

2. Taylor expanded in x around inf 49.5%

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

3. Final simplification 49.5%

   \[\leadsto x \]

Developer target: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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