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

Percentage Accurate: 85.3% → 98.1%

Time: 8.3s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

   1. associate-/l* 96.6%

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

3. Simplified 96.6%

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

   1. *-commutative 96.6%

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

   2. sub-neg 96.6%

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

   3. distribute-lft-in 94.2%

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

6. Applied egg-rr 94.2%

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

7. Taylor expanded in t around -inf 98.7%

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

   1. mul-1-neg 98.7%

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

   2. *-commutative 98.7%

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

   3. distribute-rgt-neg-in 98.7%

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

   4. +-commutative 98.7%

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

   5. mul-1-neg 98.7%

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

   6. unsub-neg 98.7%

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

9. Simplified 98.7%

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

10. Final simplification 98.7%

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

Alternative 2: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -85000000 \lor \neg \left(z \leq 96000000000\right):\\ \;\;\;\;x + \left(t - y \cdot \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - z} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -85000000.0) (not (<= z 96000000000.0)))
   (+ x (- t (* y (/ t z))))
   (+ x (* (/ y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -85000000.0) || !(z <= 96000000000.0)) {
		tmp = x + (t - (y * (t / z)));
	} else {
		tmp = x + ((y / (a - z)) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-85000000.0d0)) .or. (.not. (z <= 96000000000.0d0))) then
        tmp = x + (t - (y * (t / z)))
    else
        tmp = x + ((y / (a - z)) * 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 ((z <= -85000000.0) || !(z <= 96000000000.0)) {
		tmp = x + (t - (y * (t / z)));
	} else {
		tmp = x + ((y / (a - z)) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -85000000.0) or not (z <= 96000000000.0):
		tmp = x + (t - (y * (t / z)))
	else:
		tmp = x + ((y / (a - z)) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -85000000.0) || !(z <= 96000000000.0))
		tmp = Float64(x + Float64(t - Float64(y * Float64(t / z))));
	else
		tmp = Float64(x + Float64(Float64(y / Float64(a - z)) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -85000000.0) || ~((z <= 96000000000.0)))
		tmp = x + (t - (y * (t / z)));
	else
		tmp = x + ((y / (a - z)) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -85000000.0], N[Not[LessEqual[z, 96000000000.0]], $MachinePrecision]], N[(x + N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5e7 or 9.6e10 < z

   1. Initial program 73.8%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

      1. *-commutative 97.4%

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

      2. sub-neg 97.4%

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

      3. distribute-lft-in 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in a around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. unsub-neg 75.8%

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

      3. associate-/l* 85.9%

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

   9. Simplified 85.9%

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

   10. Taylor expanded in t around 0 75.8%

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

       1. *-commutative 75.8%

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

       2. associate-/l* 86.0%

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

   12. Simplified 86.0%

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

   if -8.5e7 < z < 9.6e10

   1. Initial program 97.2%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in y around inf 92.6%

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

      1. associate-/l* 93.3%

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

   7. Simplified 93.3%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -85000000 \lor \neg \left(z \leq 96000000000\right):\\ \;\;\;\;x + \left(t - y \cdot \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - z} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -265000000 \lor \neg \left(z \leq 1.3 \cdot 10^{+44}\right):\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - z} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -265000000.0) (not (<= z 1.3e+44)))
   (+ x (- t (* t (/ y z))))
   (+ x (* (/ y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -265000000.0) || !(z <= 1.3e+44)) {
		tmp = x + (t - (t * (y / z)));
	} else {
		tmp = x + ((y / (a - z)) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-265000000.0d0)) .or. (.not. (z <= 1.3d+44))) then
        tmp = x + (t - (t * (y / z)))
    else
        tmp = x + ((y / (a - z)) * 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 ((z <= -265000000.0) || !(z <= 1.3e+44)) {
		tmp = x + (t - (t * (y / z)));
	} else {
		tmp = x + ((y / (a - z)) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -265000000.0) or not (z <= 1.3e+44):
		tmp = x + (t - (t * (y / z)))
	else:
		tmp = x + ((y / (a - z)) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -265000000.0) || !(z <= 1.3e+44))
		tmp = Float64(x + Float64(t - Float64(t * Float64(y / z))));
	else
		tmp = Float64(x + Float64(Float64(y / Float64(a - z)) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -265000000.0) || ~((z <= 1.3e+44)))
		tmp = x + (t - (t * (y / z)));
	else
		tmp = x + ((y / (a - z)) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -265000000.0], N[Not[LessEqual[z, 1.3e+44]], $MachinePrecision]], N[(x + N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.65e8 or 1.3e44 < z

   1. Initial program 72.1%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

      1. *-commutative 97.2%

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

      2. sub-neg 97.2%

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

      3. distribute-lft-in 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in a around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

      3. associate-/l* 86.5%

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

   9. Simplified 86.5%

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

   if -2.65e8 < z < 1.3e44

   1. Initial program 96.8%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around inf 91.9%

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

      1. associate-/l* 92.5%

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

   7. Simplified 92.5%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -265000000 \lor \neg \left(z \leq 1.3 \cdot 10^{+44}\right):\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - z} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+115} \lor \neg \left(z \leq 2.2 \cdot 10^{+48}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - z} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.1e+115) (not (<= z 2.2e+48)))
   (+ x t)
   (+ x (* (/ y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e+115) || !(z <= 2.2e+48)) {
		tmp = x + t;
	} else {
		tmp = x + ((y / (a - z)) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.1d+115)) .or. (.not. (z <= 2.2d+48))) then
        tmp = x + t
    else
        tmp = x + ((y / (a - z)) * 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 ((z <= -2.1e+115) || !(z <= 2.2e+48)) {
		tmp = x + t;
	} else {
		tmp = x + ((y / (a - z)) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.1e+115) or not (z <= 2.2e+48):
		tmp = x + t
	else:
		tmp = x + ((y / (a - z)) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.1e+115) || !(z <= 2.2e+48))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(Float64(y / Float64(a - z)) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.1e+115) || ~((z <= 2.2e+48)))
		tmp = x + t;
	else
		tmp = x + ((y / (a - z)) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.1e+115], N[Not[LessEqual[z, 2.2e+48]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.10000000000000003e115 or 2.1999999999999999e48 < z

   1. Initial program 67.1%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around inf 86.3%

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

   if -2.10000000000000003e115 < z < 2.1999999999999999e48

   1. Initial program 95.7%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in y around inf 87.6%

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

      1. associate-/l* 89.2%

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

   7. Simplified 89.2%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+115} \lor \neg \left(z \leq 2.2 \cdot 10^{+48}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - z} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-178}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 3600000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.3e-178)
   (+ x t)
   (if (<= z 3.7e-247) (* y (/ t (- a z))) (if (<= z 3600000.0) x (+ x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.3e-178) {
		tmp = x + t;
	} else if (z <= 3.7e-247) {
		tmp = y * (t / (a - z));
	} else if (z <= 3600000.0) {
		tmp = x;
	} else {
		tmp = x + 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 (z <= (-4.3d-178)) then
        tmp = x + t
    else if (z <= 3.7d-247) then
        tmp = y * (t / (a - z))
    else if (z <= 3600000.0d0) then
        tmp = x
    else
        tmp = x + 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 (z <= -4.3e-178) {
		tmp = x + t;
	} else if (z <= 3.7e-247) {
		tmp = y * (t / (a - z));
	} else if (z <= 3600000.0) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.3e-178:
		tmp = x + t
	elif z <= 3.7e-247:
		tmp = y * (t / (a - z))
	elif z <= 3600000.0:
		tmp = x
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.3e-178)
		tmp = Float64(x + t);
	elseif (z <= 3.7e-247)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= 3600000.0)
		tmp = x;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.3e-178)
		tmp = x + t;
	elseif (z <= 3.7e-247)
		tmp = y * (t / (a - z));
	elseif (z <= 3600000.0)
		tmp = x;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.3e-178], N[(x + t), $MachinePrecision], If[LessEqual[z, 3.7e-247], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3600000.0], x, N[(x + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3e-178 or 3.6e6 < z

   1. Initial program 80.6%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around inf 70.2%

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

   if -4.3e-178 < z < 3.7000000000000001e-247

   1. Initial program 92.6%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in y around inf 90.7%

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

   6. Taylor expanded in x around 0 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-*r/ 67.5%

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

   8. Simplified 67.5%

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

   if 3.7000000000000001e-247 < z < 3.6e6

   1. Initial program 99.9%

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

      1. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in y around inf 98.1%

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

      1. associate-/l* 94.6%

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

   7. Simplified 94.6%

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

   8. Taylor expanded in x around inf 66.9%

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

Alternative 6: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+115} \lor \neg \left(z \leq 15800000000\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+115) (not (<= z 15800000000.0)))
   (+ x t)
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+115) || !(z <= 15800000000.0)) {
		tmp = x + t;
	} 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 <= (-1.45d+115)) .or. (.not. (z <= 15800000000.0d0))) then
        tmp = x + t
    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 <= -1.45e+115) || !(z <= 15800000000.0)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+115) or not (z <= 15800000000.0):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+115) || !(z <= 15800000000.0))
		tmp = Float64(x + t);
	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 <= -1.45e+115) || ~((z <= 15800000000.0)))
		tmp = x + t;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e+115], N[Not[LessEqual[z, 15800000000.0]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45000000000000002e115 or 1.58e10 < z

   1. Initial program 69.8%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around inf 83.3%

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

   if -1.45000000000000002e115 < z < 1.58e10

   1. Initial program 95.9%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in y around inf 88.1%

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

      1. associate-/l* 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in a around inf 76.9%

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

      1. +-commutative 76.9%

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

      2. associate-/l* 79.1%

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

   10. Simplified 79.1%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+115} \lor \neg \left(z \leq 15800000000\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+115} \lor \neg \left(z \leq 118000000\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+115) (not (<= z 118000000.0)))
   (+ x t)
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+115) || !(z <= 118000000.0)) {
		tmp = x + t;
	} 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 <= (-1.45d+115)) .or. (.not. (z <= 118000000.0d0))) then
        tmp = x + t
    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 <= -1.45e+115) || !(z <= 118000000.0)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+115) or not (z <= 118000000.0):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+115) || !(z <= 118000000.0))
		tmp = Float64(x + t);
	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 <= -1.45e+115) || ~((z <= 118000000.0)))
		tmp = x + t;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e+115], N[Not[LessEqual[z, 118000000.0]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45000000000000002e115 or 1.18e8 < z

   1. Initial program 69.8%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around inf 83.3%

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

   if -1.45000000000000002e115 < z < 1.18e8

   1. Initial program 95.9%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around 0 76.9%

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

      1. associate-/l* 79.1%

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

   7. Simplified 79.1%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+115} \lor \neg \left(z \leq 118000000\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-62} \lor \neg \left(z \leq 52000000\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.05e-62) (not (<= z 52000000.0))) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.05e-62) || !(z <= 52000000.0)) {
		tmp = x + t;
	} 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) :: tmp
    if ((z <= (-2.05d-62)) .or. (.not. (z <= 52000000.0d0))) then
        tmp = x + t
    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 tmp;
	if ((z <= -2.05e-62) || !(z <= 52000000.0)) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.05e-62) or not (z <= 52000000.0):
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.05e-62) || !(z <= 52000000.0))
		tmp = Float64(x + t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.05e-62) || ~((z <= 52000000.0)))
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.05e-62], N[Not[LessEqual[z, 52000000.0]], $MachinePrecision]], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.05e-62 or 5.2e7 < z

   1. Initial program 77.1%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around inf 72.5%

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

   if -2.05e-62 < z < 5.2e7

   1. Initial program 96.9%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around inf 94.0%

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

      1. associate-/l* 94.7%

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

   7. Simplified 94.7%

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

   8. Taylor expanded in x around inf 52.7%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-62} \lor \neg \left(z \leq 52000000\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.5% accurate, 1.0× speedup

Math

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

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(Float64(y - z) * Float64(t / Float64(z - a))))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

   1. associate-/l* 96.6%

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

3. Simplified 96.6%

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

5. Final simplification 96.6%

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

Alternative 10: 50.1% 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 87.1%

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

   1. associate-/l* 96.6%

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

3. Simplified 96.6%

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

5. Taylor expanded in y around inf 76.9%

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

   1. associate-/l* 79.3%

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

7. Simplified 79.3%

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

8. Taylor expanded in x around inf 50.2%

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

Developer target: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - z) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024103 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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