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

Percentage Accurate: 98.0% → 98.8%

Time: 12.5s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- a z))))
   (if (<= t_1 (- INFINITY)) (+ x (/ (* y t) (- a z))) (+ x (* y t_1)))))

C

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

Java

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

Python

def code(x, y, z, t, a):
	t_1 = (t - z) / (a - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((y * t) / (a - z))
	else:
		tmp = x + (y * t_1)
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -inf.0

   1. Initial program 52.7%

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

   3. Taylor expanded in t around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around 0 99.7%

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

   if -inf.0 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 98.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 59.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+86}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+158}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+215} \lor \neg \left(t \leq 1.65 \cdot 10^{+220}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t a))))
   (if (<= t -2.6e+272)
     t_1
     (if (<= t 1.15e+86)
       (+ x y)
       (if (<= t 9.4e+148)
         t_1
         (if (<= t 2.6e+158)
           (+ x y)
           (if (or (<= t 2.7e+215) (not (<= t 1.65e+220))) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (t <= -2.6e+272) {
		tmp = t_1;
	} else if (t <= 1.15e+86) {
		tmp = x + y;
	} else if (t <= 9.4e+148) {
		tmp = t_1;
	} else if (t <= 2.6e+158) {
		tmp = x + y;
	} else if ((t <= 2.7e+215) || !(t <= 1.65e+220)) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = y * (t / a)
    if (t <= (-2.6d+272)) then
        tmp = t_1
    else if (t <= 1.15d+86) then
        tmp = x + y
    else if (t <= 9.4d+148) then
        tmp = t_1
    else if (t <= 2.6d+158) then
        tmp = x + y
    else if ((t <= 2.7d+215) .or. (.not. (t <= 1.65d+220))) then
        tmp = t_1
    else
        tmp = x
    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 * (t / a);
	double tmp;
	if (t <= -2.6e+272) {
		tmp = t_1;
	} else if (t <= 1.15e+86) {
		tmp = x + y;
	} else if (t <= 9.4e+148) {
		tmp = t_1;
	} else if (t <= 2.6e+158) {
		tmp = x + y;
	} else if ((t <= 2.7e+215) || !(t <= 1.65e+220)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / a)
	tmp = 0
	if t <= -2.6e+272:
		tmp = t_1
	elif t <= 1.15e+86:
		tmp = x + y
	elif t <= 9.4e+148:
		tmp = t_1
	elif t <= 2.6e+158:
		tmp = x + y
	elif (t <= 2.7e+215) or not (t <= 1.65e+220):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / a))
	tmp = 0.0
	if (t <= -2.6e+272)
		tmp = t_1;
	elseif (t <= 1.15e+86)
		tmp = Float64(x + y);
	elseif (t <= 9.4e+148)
		tmp = t_1;
	elseif (t <= 2.6e+158)
		tmp = Float64(x + y);
	elseif ((t <= 2.7e+215) || !(t <= 1.65e+220))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / a);
	tmp = 0.0;
	if (t <= -2.6e+272)
		tmp = t_1;
	elseif (t <= 1.15e+86)
		tmp = x + y;
	elseif (t <= 9.4e+148)
		tmp = t_1;
	elseif (t <= 2.6e+158)
		tmp = x + y;
	elseif ((t <= 2.7e+215) || ~((t <= 1.65e+220)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e+272], t$95$1, If[LessEqual[t, 1.15e+86], N[(x + y), $MachinePrecision], If[LessEqual[t, 9.4e+148], t$95$1, If[LessEqual[t, 2.6e+158], N[(x + y), $MachinePrecision], If[Or[LessEqual[t, 2.7e+215], N[Not[LessEqual[t, 1.65e+220]], $MachinePrecision]], t$95$1, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.59999999999999999e272 or 1.14999999999999995e86 < t < 9.3999999999999994e148 or 2.6e158 < t < 2.7e215 or 1.65000000000000011e220 < t

   1. Initial program 94.1%

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

   3. Taylor expanded in t around inf 78.5%

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

      1. mul-1-neg 78.5%

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

      2. associate-/l* 93.9%

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

   5. Simplified 93.9%

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

   6. Taylor expanded in x around 0 78.5%

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

   7. Taylor expanded in x around inf 68.8%

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

      1. mul-1-neg 68.8%

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

      2. unsub-neg 68.8%

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

      3. associate-/l* 80.4%

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

      4. associate-/r* 78.4%

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

   9. Simplified 78.4%

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

   10. Taylor expanded in x around 0 66.2%

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

       1. associate-*r/ 66.2%

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

       2. associate-*r* 66.2%

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

       3. neg-mul-1 66.2%

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

       4. *-commutative 66.2%

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

   12. Simplified 66.2%

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

   13. Taylor expanded in z around 0 50.1%

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

       1. *-commutative 50.1%

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

       2. associate-/l* 61.5%

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

   15. Simplified 61.5%

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

   if -2.59999999999999999e272 < t < 1.14999999999999995e86 or 9.3999999999999994e148 < t < 2.6e158

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 66.8%

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

   if 2.7e215 < t < 1.65000000000000011e220

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 100.0%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+272}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+86}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+158}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+215} \lor \neg \left(t \leq 1.65 \cdot 10^{+220}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{y}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+156}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+234}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= z -1.5e+91)
     t_1
     (if (<= z 7e-23)
       (+ x (/ (* y t) (- a z)))
       (if (<= z 8.5e+136)
         (- x (/ y (/ (- a z) z)))
         (if (<= z 1.6e+156)
           (+ x (* t (/ y a)))
           (if (<= z 5e+234) (+ x (* y (/ z (- z a)))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -1.5e+91) {
		tmp = t_1;
	} else if (z <= 7e-23) {
		tmp = x + ((y * t) / (a - z));
	} else if (z <= 8.5e+136) {
		tmp = x - (y / ((a - z) / z));
	} else if (z <= 1.6e+156) {
		tmp = x + (t * (y / a));
	} else if (z <= 5e+234) {
		tmp = x + (y * (z / (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) :: tmp
    t_1 = x + (y * (1.0d0 - (t / z)))
    if (z <= (-1.5d+91)) then
        tmp = t_1
    else if (z <= 7d-23) then
        tmp = x + ((y * t) / (a - z))
    else if (z <= 8.5d+136) then
        tmp = x - (y / ((a - z) / z))
    else if (z <= 1.6d+156) then
        tmp = x + (t * (y / a))
    else if (z <= 5d+234) then
        tmp = x + (y * (z / (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 * (1.0 - (t / z)));
	double tmp;
	if (z <= -1.5e+91) {
		tmp = t_1;
	} else if (z <= 7e-23) {
		tmp = x + ((y * t) / (a - z));
	} else if (z <= 8.5e+136) {
		tmp = x - (y / ((a - z) / z));
	} else if (z <= 1.6e+156) {
		tmp = x + (t * (y / a));
	} else if (z <= 5e+234) {
		tmp = x + (y * (z / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if z <= -1.5e+91:
		tmp = t_1
	elif z <= 7e-23:
		tmp = x + ((y * t) / (a - z))
	elif z <= 8.5e+136:
		tmp = x - (y / ((a - z) / z))
	elif z <= 1.6e+156:
		tmp = x + (t * (y / a))
	elif z <= 5e+234:
		tmp = x + (y * (z / (z - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (z <= -1.5e+91)
		tmp = t_1;
	elseif (z <= 7e-23)
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	elseif (z <= 8.5e+136)
		tmp = Float64(x - Float64(y / Float64(Float64(a - z) / z)));
	elseif (z <= 1.6e+156)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 5e+234)
		tmp = Float64(x + Float64(y * Float64(z / 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 * (1.0 - (t / z)));
	tmp = 0.0;
	if (z <= -1.5e+91)
		tmp = t_1;
	elseif (z <= 7e-23)
		tmp = x + ((y * t) / (a - z));
	elseif (z <= 8.5e+136)
		tmp = x - (y / ((a - z) / z));
	elseif (z <= 1.6e+156)
		tmp = x + (t * (y / a));
	elseif (z <= 5e+234)
		tmp = x + (y * (z / (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[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+91], t$95$1, If[LessEqual[z, 7e-23], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+136], N[(x - N[(y / N[(N[(a - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+156], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+234], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.50000000000000003e91 or 5.0000000000000003e234 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 59.6%

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

      1. associate-/l* 92.5%

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

      2. div-sub 92.5%

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

      3. *-inverses 92.5%

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

   5. Simplified 92.5%

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

   if -1.50000000000000003e91 < z < 6.99999999999999987e-23

   1. Initial program 94.8%

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

   3. Taylor expanded in t around inf 85.6%

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

      1. mul-1-neg 85.6%

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

      2. associate-/l* 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in x around 0 85.6%

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

   if 6.99999999999999987e-23 < z < 8.49999999999999966e136

   1. Initial program 99.9%

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

      1. clear-num 100.0%

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

      2. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0 83.7%

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

   if 8.49999999999999966e136 < z < 1.60000000000000001e156

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   if 1.60000000000000001e156 < z < 5.0000000000000003e234

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 53.1%

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

      1. associate-/l* 95.3%

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

   5. Simplified 95.3%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{z - a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+91}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+136}:\\ \;\;\;\;x - \frac{y}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+156}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+234}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -6.3 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-195}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 10^{-252}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-55}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= z -6.3e-18)
     (+ x (/ y (- 1.0 (/ a z))))
     (if (<= z -2.9e-186)
       t_1
       (if (<= z -6.2e-195)
         (* t (/ y (- a z)))
         (if (<= z 1e-252)
           t_1
           (if (<= z 5.5e-55)
             (+ x (* y (/ t a)))
             (+ x (* y (/ z (- z a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (z <= -6.3e-18) {
		tmp = x + (y / (1.0 - (a / z)));
	} else if (z <= -2.9e-186) {
		tmp = t_1;
	} else if (z <= -6.2e-195) {
		tmp = t * (y / (a - z));
	} else if (z <= 1e-252) {
		tmp = t_1;
	} else if (z <= 5.5e-55) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	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 = x + (t * (y / a))
    if (z <= (-6.3d-18)) then
        tmp = x + (y / (1.0d0 - (a / z)))
    else if (z <= (-2.9d-186)) then
        tmp = t_1
    else if (z <= (-6.2d-195)) then
        tmp = t * (y / (a - z))
    else if (z <= 1d-252) then
        tmp = t_1
    else if (z <= 5.5d-55) then
        tmp = x + (y * (t / a))
    else
        tmp = x + (y * (z / (z - a)))
    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 + (t * (y / a));
	double tmp;
	if (z <= -6.3e-18) {
		tmp = x + (y / (1.0 - (a / z)));
	} else if (z <= -2.9e-186) {
		tmp = t_1;
	} else if (z <= -6.2e-195) {
		tmp = t * (y / (a - z));
	} else if (z <= 1e-252) {
		tmp = t_1;
	} else if (z <= 5.5e-55) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if z <= -6.3e-18:
		tmp = x + (y / (1.0 - (a / z)))
	elif z <= -2.9e-186:
		tmp = t_1
	elif z <= -6.2e-195:
		tmp = t * (y / (a - z))
	elif z <= 1e-252:
		tmp = t_1
	elif z <= 5.5e-55:
		tmp = x + (y * (t / a))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (z <= -6.3e-18)
		tmp = Float64(x + Float64(y / Float64(1.0 - Float64(a / z))));
	elseif (z <= -2.9e-186)
		tmp = t_1;
	elseif (z <= -6.2e-195)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1e-252)
		tmp = t_1;
	elseif (z <= 5.5e-55)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (z <= -6.3e-18)
		tmp = x + (y / (1.0 - (a / z)));
	elseif (z <= -2.9e-186)
		tmp = t_1;
	elseif (z <= -6.2e-195)
		tmp = t * (y / (a - z));
	elseif (z <= 1e-252)
		tmp = t_1;
	elseif (z <= 5.5e-55)
		tmp = x + (y * (t / a));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.3e-18], N[(x + N[(y / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-186], t$95$1, If[LessEqual[z, -6.2e-195], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-252], t$95$1, If[LessEqual[z, 5.5e-55], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.3000000000000004e-18

   1. Initial program 99.8%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 85.7%

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

      1. div-sub 85.7%

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

      2. *-inverses 85.7%

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

   7. Simplified 85.7%

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

   if -6.3000000000000004e-18 < z < -2.90000000000000019e-186 or -6.20000000000000005e-195 < z < 9.99999999999999943e-253

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 82.0%

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

      1. associate-/l* 87.4%

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

   5. Simplified 87.4%

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

   if -2.90000000000000019e-186 < z < -6.20000000000000005e-195

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 76.3%

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

   7. Taylor expanded in x around 0 76.3%

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

      1. associate-*r/ 76.3%

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

      2. mul-1-neg 76.3%

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

      3. distribute-rgt-neg-in 76.3%

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

      4. associate-*r/ 100.0%

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

   9. Simplified 100.0%

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

   if 9.99999999999999943e-253 < z < 5.4999999999999999e-55

   1. Initial program 92.1%

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

   3. Taylor expanded in z around 0 70.1%

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

      1. *-commutative 70.1%

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

      2. associate-/l* 77.5%

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

   5. Simplified 77.5%

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

   if 5.4999999999999999e-55 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 65.4%

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

      1. associate-/l* 83.9%

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

   5. Simplified 83.9%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{z - a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y}{1 - \frac{a}{z}}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-186}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-195}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 10^{-252}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-55}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -1.2e-45)
     t_2
     (if (<= a 3e-166)
       t_1
       (if (<= a 4.5e-139)
         (* t (/ y (- a z)))
         (if (<= a 1.55e-53) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -1.2e-45) {
		tmp = t_2;
	} else if (a <= 3e-166) {
		tmp = t_1;
	} else if (a <= 4.5e-139) {
		tmp = t * (y / (a - z));
	} else if (a <= 1.55e-53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = x + (y * (1.0d0 - (t / z)))
    t_2 = x + (t * (y / a))
    if (a <= (-1.2d-45)) then
        tmp = t_2
    else if (a <= 3d-166) then
        tmp = t_1
    else if (a <= 4.5d-139) then
        tmp = t * (y / (a - z))
    else if (a <= 1.55d-53) then
        tmp = t_1
    else
        tmp = t_2
    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 * (1.0 - (t / z)));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -1.2e-45) {
		tmp = t_2;
	} else if (a <= 3e-166) {
		tmp = t_1;
	} else if (a <= 4.5e-139) {
		tmp = t * (y / (a - z));
	} else if (a <= 1.55e-53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	t_2 = x + (t * (y / a))
	tmp = 0
	if a <= -1.2e-45:
		tmp = t_2
	elif a <= 3e-166:
		tmp = t_1
	elif a <= 4.5e-139:
		tmp = t * (y / (a - z))
	elif a <= 1.55e-53:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.2e-45)
		tmp = t_2;
	elseif (a <= 3e-166)
		tmp = t_1;
	elseif (a <= 4.5e-139)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (a <= 1.55e-53)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (t / z)));
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -1.2e-45)
		tmp = t_2;
	elseif (a <= 3e-166)
		tmp = t_1;
	elseif (a <= 4.5e-139)
		tmp = t * (y / (a - z));
	elseif (a <= 1.55e-53)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e-45], t$95$2, If[LessEqual[a, 3e-166], t$95$1, If[LessEqual[a, 4.5e-139], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e-53], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.19999999999999995e-45 or 1.55000000000000008e-53 < a

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 73.0%

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

      1. associate-/l* 79.6%

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

   5. Simplified 79.6%

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

   if -1.19999999999999995e-45 < a < 3.0000000000000003e-166 or 4.50000000000000023e-139 < a < 1.55000000000000008e-53

   1. Initial program 95.8%

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

   3. Taylor expanded in a around 0 71.9%

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

      1. associate-/l* 83.9%

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

      2. div-sub 83.9%

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

      3. *-inverses 83.9%

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

   5. Simplified 83.9%

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

   if 3.0000000000000003e-166 < a < 4.50000000000000023e-139

   1. Initial program 42.7%

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

   3. Taylor expanded in t around inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around 0 99.4%

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

   7. Taylor expanded in x around 0 99.4%

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

      1. associate-*r/ 99.4%

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

      2. mul-1-neg 99.4%

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

      3. distribute-rgt-neg-in 99.4%

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

      4. associate-*r/ 99.7%

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

   9. Simplified 99.7%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-45}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-166}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-53}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-44}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+153)
   (+ x (/ y (/ z (- z t))))
   (if (<= z 2.9e-44) (+ x (* t (/ y (- a z)))) (+ x (* y (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+153) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 2.9e-44) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	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 (z <= (-1.9d+153)) then
        tmp = x + (y / (z / (z - t)))
    else if (z <= 2.9d-44) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (y * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+153) {
		tmp = x + (y / (z / (z - t)));
	} else if (z <= 2.9e-44) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+153:
		tmp = x + (y / (z / (z - t)))
	elif z <= 2.9e-44:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (y * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+153)
		tmp = Float64(x + Float64(y / Float64(z / Float64(z - t))));
	elseif (z <= 2.9e-44)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e+153)
		tmp = x + (y / (z / (z - t)));
	elseif (z <= 2.9e-44)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (y * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+153], N[(x + N[(y / N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-44], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.89999999999999983e153

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in a around 0 93.2%

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

   if -1.89999999999999983e153 < z < 2.9000000000000001e-44

   1. Initial program 95.0%

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

   3. Taylor expanded in t around inf 84.6%

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

      1. mul-1-neg 84.6%

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

      2. associate-/l* 89.6%

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

   5. Simplified 89.6%

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

   if 2.9000000000000001e-44 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 65.8%

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

      1. associate-/l* 85.8%

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

   5. Simplified 85.8%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-44}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+153} \lor \neg \left(z \leq 5 \cdot 10^{-55}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e+153) (not (<= z 5e-55))) (+ x y) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+153) || !(z <= 5e-55)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	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 ((z <= (-1.9d+153)) .or. (.not. (z <= 5d-55))) then
        tmp = x + y
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+153) || !(z <= 5e-55)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.9e+153) or not (z <= 5e-55):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e+153) || !(z <= 5e-55))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.9e+153) || ~((z <= 5e-55)))
		tmp = x + y;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.9e+153], N[Not[LessEqual[z, 5e-55]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.89999999999999983e153 or 5.0000000000000002e-55 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 77.3%

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

   if -1.89999999999999983e153 < z < 5.0000000000000002e-55

   1. Initial program 94.9%

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

   3. Taylor expanded in z around 0 73.1%

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

      1. associate-/l* 78.1%

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

   5. Simplified 78.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+153} \lor \neg \left(z \leq 5 \cdot 10^{-55}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.2% accurate, 1.0× 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]

Derivation

1. Initial program 96.9%

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

   1. clear-num 96.9%

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

   2. un-div-inv 97.5%

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

4. Applied egg-rr 97.5%

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

Alternative 9: 59.9% accurate, 3.7× 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 96.9%

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

3. Taylor expanded in z around inf 57.5%

   \[\leadsto x + \color{blue}{y} \]
4. Add Preprocessing

Alternative 10: 50.4% 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 96.9%

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

3. Taylor expanded in t around inf 73.6%

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

   1. mul-1-neg 73.6%

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

   2. associate-/l* 76.7%

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

5. Simplified 76.7%

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

6. Taylor expanded in x around inf 47.5%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Developer target: 98.2% accurate, 1.0× 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 2024107 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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