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

Percentage Accurate: 85.0% → 98.3%

Time: 7.6s

Alternatives: 11

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: 85.0% 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: 98.3% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 83.1%

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

   1. associate-*l/ 98.5%

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

3. Simplified 98.5%

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

4. Final simplification 98.5%

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

Alternative 2: 76.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{-z}{t}}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+175}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ (- z) t)))))
   (if (<= z -6e+175)
     (+ x t)
     (if (<= z -2.35e+39)
       t_1
       (if (<= z 5000000.0)
         (+ x (/ y (/ a t)))
         (if (<= z 8e+121) t_1 (+ x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (-z / t));
	double tmp;
	if (z <= -6e+175) {
		tmp = x + t;
	} else if (z <= -2.35e+39) {
		tmp = t_1;
	} else if (z <= 5000000.0) {
		tmp = x + (y / (a / t));
	} else if (z <= 8e+121) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (-z / t))
    if (z <= (-6d+175)) then
        tmp = x + t
    else if (z <= (-2.35d+39)) then
        tmp = t_1
    else if (z <= 5000000.0d0) then
        tmp = x + (y / (a / t))
    else if (z <= 8d+121) then
        tmp = t_1
    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 t_1 = x + (y / (-z / t));
	double tmp;
	if (z <= -6e+175) {
		tmp = x + t;
	} else if (z <= -2.35e+39) {
		tmp = t_1;
	} else if (z <= 5000000.0) {
		tmp = x + (y / (a / t));
	} else if (z <= 8e+121) {
		tmp = t_1;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (-z / t))
	tmp = 0
	if z <= -6e+175:
		tmp = x + t
	elif z <= -2.35e+39:
		tmp = t_1
	elif z <= 5000000.0:
		tmp = x + (y / (a / t))
	elif z <= 8e+121:
		tmp = t_1
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(Float64(-z) / t)))
	tmp = 0.0
	if (z <= -6e+175)
		tmp = Float64(x + t);
	elseif (z <= -2.35e+39)
		tmp = t_1;
	elseif (z <= 5000000.0)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 8e+121)
		tmp = t_1;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (-z / t));
	tmp = 0.0;
	if (z <= -6e+175)
		tmp = x + t;
	elseif (z <= -2.35e+39)
		tmp = t_1;
	elseif (z <= 5000000.0)
		tmp = x + (y / (a / t));
	elseif (z <= 8e+121)
		tmp = t_1;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[((-z) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+175], N[(x + t), $MachinePrecision], If[LessEqual[z, -2.35e+39], t$95$1, If[LessEqual[z, 5000000.0], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+121], t$95$1, N[(x + t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0000000000000003e175 or 8.0000000000000003e121 < z

   1. Initial program 53.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 95.2%

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

   if -6.0000000000000003e175 < z < -2.35e39 or 5e6 < z < 8.0000000000000003e121

   1. Initial program 83.3%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 72.3%

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

      1. associate-/l* 81.5%

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

   6. Simplified 81.5%

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

   7. Taylor expanded in a around 0 75.5%

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

      1. neg-mul-1 75.5%

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

      2. distribute-neg-frac 75.5%

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

   9. Simplified 75.5%

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

   if -2.35e39 < z < 5e6

   1. Initial program 95.3%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 78.8%

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

      1. associate-/l* 82.0%

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

   6. Simplified 82.0%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+175}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;z \leq 5000000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+121}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 3: 76.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+174}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3900000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ y z)))))
   (if (<= z -2e+174)
     (+ x t)
     (if (<= z -5.1e+38)
       t_1
       (if (<= z 3900000.0)
         (+ x (/ y (/ a t)))
         (if (<= z 1.85e+121) t_1 (+ x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / z));
	double tmp;
	if (z <= -2e+174) {
		tmp = x + t;
	} else if (z <= -5.1e+38) {
		tmp = t_1;
	} else if (z <= 3900000.0) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.85e+121) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (t * (y / z))
    if (z <= (-2d+174)) then
        tmp = x + t
    else if (z <= (-5.1d+38)) then
        tmp = t_1
    else if (z <= 3900000.0d0) then
        tmp = x + (y / (a / t))
    else if (z <= 1.85d+121) then
        tmp = t_1
    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 t_1 = x - (t * (y / z));
	double tmp;
	if (z <= -2e+174) {
		tmp = x + t;
	} else if (z <= -5.1e+38) {
		tmp = t_1;
	} else if (z <= 3900000.0) {
		tmp = x + (y / (a / t));
	} else if (z <= 1.85e+121) {
		tmp = t_1;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (y / z))
	tmp = 0
	if z <= -2e+174:
		tmp = x + t
	elif z <= -5.1e+38:
		tmp = t_1
	elif z <= 3900000.0:
		tmp = x + (y / (a / t))
	elif z <= 1.85e+121:
		tmp = t_1
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (z <= -2e+174)
		tmp = Float64(x + t);
	elseif (z <= -5.1e+38)
		tmp = t_1;
	elseif (z <= 3900000.0)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 1.85e+121)
		tmp = t_1;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (y / z));
	tmp = 0.0;
	if (z <= -2e+174)
		tmp = x + t;
	elseif (z <= -5.1e+38)
		tmp = t_1;
	elseif (z <= 3900000.0)
		tmp = x + (y / (a / t));
	elseif (z <= 1.85e+121)
		tmp = t_1;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+174], N[(x + t), $MachinePrecision], If[LessEqual[z, -5.1e+38], t$95$1, If[LessEqual[z, 3900000.0], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+121], t$95$1, N[(x + t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.00000000000000014e174 or 1.85000000000000006e121 < z

   1. Initial program 53.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 95.2%

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

   if -2.00000000000000014e174 < z < -5.1000000000000001e38 or 3.9e6 < z < 1.85000000000000006e121

   1. Initial program 83.3%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 81.4%

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

   5. Taylor expanded in a around 0 75.4%

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

      1. associate-*r/ 75.4%

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

      2. neg-mul-1 75.4%

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

   7. Simplified 75.4%

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

   if -5.1000000000000001e38 < z < 3.9e6

   1. Initial program 95.3%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 78.8%

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

      1. associate-/l* 82.0%

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

   6. Simplified 82.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+174}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{+38}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 3900000:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+121}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 4: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+86} \lor \neg \left(z \leq 6800000000\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.3e+86) (not (<= z 6800000000.0)))
   (+ x (* t (- 1.0 (/ y z))))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.3e+86) || !(z <= 6800000000.0)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (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 ((z <= (-4.3d+86)) .or. (.not. (z <= 6800000000.0d0))) then
        tmp = x + (t * (1.0d0 - (y / z)))
    else
        tmp = x + (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 ((z <= -4.3e+86) || !(z <= 6800000000.0)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.3e+86) or not (z <= 6800000000.0):
		tmp = x + (t * (1.0 - (y / z)))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.3e+86) || !(z <= 6800000000.0))
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.3e+86) || ~((z <= 6800000000.0)))
		tmp = x + (t * (1.0 - (y / z)));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.3e+86], N[Not[LessEqual[z, 6800000000.0]], $MachinePrecision]], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3000000000000002e86 or 6.8e9 < z

   1. Initial program 66.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 91.7%

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

      1. associate-*r/ 91.7%

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

      2. neg-mul-1 91.7%

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

      3. neg-sub0 91.7%

         \[\leadsto x + \frac{\color{blue}{0 - \left(y - z\right)}}{z} \cdot t \]

      4. associate--r- 91.7%

         \[\leadsto x + \frac{\color{blue}{\left(0 - y\right) + z}}{z} \cdot t \]

      5. neg-sub0 91.7%

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

   6. Simplified 91.7%

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

   7. Taylor expanded in y around 0 91.7%

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

      1. +-commutative 91.7%

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

      2. mul-1-neg 91.7%

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

      3. unsub-neg 91.7%

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

   9. Simplified 91.7%

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

   if -4.3000000000000002e86 < z < 6.8e9

   1. Initial program 93.8%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around 0 77.5%

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

      1. associate-/l* 81.2%

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

   6. Simplified 81.2%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+86} \lor \neg \left(z \leq 6800000000\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 5: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+175} \lor \neg \left(z \leq 1.6 \cdot 10^{+68}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.6e+175) (not (<= z 1.6e+68)))
   (+ x (* t (- 1.0 (/ y z))))
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.6e+175) || !(z <= 1.6e+68)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	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 <= (-9.6d+175)) .or. (.not. (z <= 1.6d+68))) then
        tmp = x + (t * (1.0d0 - (y / z)))
    else
        tmp = x + (t * (y / (a - z)))
    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 <= -9.6e+175) || !(z <= 1.6e+68)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.6e+175) or not (z <= 1.6e+68):
		tmp = x + (t * (1.0 - (y / z)))
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.6e+175) || !(z <= 1.6e+68))
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	else
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.6e+175) || ~((z <= 1.6e+68)))
		tmp = x + (t * (1.0 - (y / z)));
	else
		tmp = x + (t * (y / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.6e+175], N[Not[LessEqual[z, 1.6e+68]], $MachinePrecision]], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.6e175 or 1.59999999999999997e68 < z

   1. Initial program 59.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 97.8%

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

      1. associate-*r/ 97.8%

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

      2. neg-mul-1 97.8%

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

      3. neg-sub0 97.8%

         \[\leadsto x + \frac{\color{blue}{0 - \left(y - z\right)}}{z} \cdot t \]

      4. associate--r- 97.8%

         \[\leadsto x + \frac{\color{blue}{\left(0 - y\right) + z}}{z} \cdot t \]

      5. neg-sub0 97.8%

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

   6. Simplified 97.8%

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

   7. Taylor expanded in y around 0 97.8%

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

      1. +-commutative 97.8%

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

      2. mul-1-neg 97.8%

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

      3. unsub-neg 97.8%

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

   9. Simplified 97.8%

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

   if -9.6e175 < z < 1.59999999999999997e68

   1. Initial program 92.3%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in y around inf 88.2%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+175} \lor \neg \left(z \leq 1.6 \cdot 10^{+68}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 6: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+174} \lor \neg \left(z \leq 1.6 \cdot 10^{+68}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.3e+174) (not (<= z 1.6e+68)))
   (+ x (* t (- 1.0 (/ y z))))
   (+ x (/ y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e+174) || !(z <= 1.6e+68)) {
		tmp = x + (t * (1.0 - (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 <= (-2.3d+174)) .or. (.not. (z <= 1.6d+68))) then
        tmp = x + (t * (1.0d0 - (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 <= -2.3e+174) || !(z <= 1.6e+68)) {
		tmp = x + (t * (1.0 - (y / z)));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.3e+174) or not (z <= 1.6e+68):
		tmp = x + (t * (1.0 - (y / z)))
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.3e+174) || !(z <= 1.6e+68))
		tmp = Float64(x + Float64(t * Float64(1.0 - Float64(y / z))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.3e+174) || ~((z <= 1.6e+68)))
		tmp = x + (t * (1.0 - (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, -2.3e+174], N[Not[LessEqual[z, 1.6e+68]], $MachinePrecision]], N[(x + N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999998e174 or 1.59999999999999997e68 < z

   1. Initial program 59.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 97.8%

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

      1. associate-*r/ 97.8%

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

      2. neg-mul-1 97.8%

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

      3. neg-sub0 97.8%

         \[\leadsto x + \frac{\color{blue}{0 - \left(y - z\right)}}{z} \cdot t \]

      4. associate--r- 97.8%

         \[\leadsto x + \frac{\color{blue}{\left(0 - y\right) + z}}{z} \cdot t \]

      5. neg-sub0 97.8%

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

   6. Simplified 97.8%

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

   7. Taylor expanded in y around 0 97.8%

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

      1. +-commutative 97.8%

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

      2. mul-1-neg 97.8%

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

      3. unsub-neg 97.8%

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

   9. Simplified 97.8%

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

   if -2.2999999999999998e174 < z < 1.59999999999999997e68

   1. Initial program 92.3%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in y around inf 84.6%

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

      1. associate-/l* 89.2%

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

   6. Simplified 89.2%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+174} \lor \neg \left(z \leq 1.6 \cdot 10^{+68}\right):\\ \;\;\;\;x + t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 7: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+111} \lor \neg \left(y \leq 2.35 \cdot 10^{+25}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.4e+111) (not (<= y 2.35e+25)))
   (+ x (/ y (/ (- a z) t)))
   (- x (* t (/ z (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.4e+111) || !(y <= 2.35e+25)) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x - (t * (z / (a - z)));
	}
	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 ((y <= (-1.4d+111)) .or. (.not. (y <= 2.35d+25))) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = x - (t * (z / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.4e+111) || !(y <= 2.35e+25)) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x - (t * (z / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.4e+111) or not (y <= 2.35e+25):
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x - (t * (z / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.4e+111) || !(y <= 2.35e+25))
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x - Float64(t * Float64(z / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.4e+111) || ~((y <= 2.35e+25)))
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x - (t * (z / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.4e+111], N[Not[LessEqual[y, 2.35e+25]], $MachinePrecision]], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e111 or 2.3499999999999999e25 < y

   1. Initial program 80.0%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in y around inf 74.4%

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

      1. associate-/l* 90.8%

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

   6. Simplified 90.8%

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

   if -1.4e111 < y < 2.3499999999999999e25

   1. Initial program 84.8%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around 0 92.3%

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

      1. neg-mul-1 92.3%

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

      2. distribute-neg-frac 92.3%

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

   6. Simplified 92.3%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+111} \lor \neg \left(y \leq 2.35 \cdot 10^{+25}\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \end{array} \]

Alternative 8: 62.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+86} \lor \neg \left(z \leq 1420000000\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+86) (not (<= z 1420000000.0))) (+ x t) (+ x (* z (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+86) || !(z <= 1420000000.0)) {
		tmp = x + t;
	} else {
		tmp = x + (z * (t / 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 <= (-4d+86)) .or. (.not. (z <= 1420000000.0d0))) then
        tmp = x + t
    else
        tmp = x + (z * (t / 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 <= -4e+86) || !(z <= 1420000000.0)) {
		tmp = x + t;
	} else {
		tmp = x + (z * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e+86) or not (z <= 1420000000.0):
		tmp = x + t
	else:
		tmp = x + (z * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+86) || !(z <= 1420000000.0))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4e+86) || ~((z <= 1420000000.0)))
		tmp = x + t;
	else
		tmp = x + (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+86], N[Not[LessEqual[z, 1420000000.0]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0000000000000001e86 or 1.42e9 < z

   1. Initial program 66.6%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 78.4%

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

   if -4.0000000000000001e86 < z < 1.42e9

   1. Initial program 93.8%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in a around inf 80.4%

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

      1. associate-/l* 83.0%

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

   6. Simplified 83.0%

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

   7. Taylor expanded in y around 0 64.3%

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

      1. associate-*r/ 64.3%

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

      2. neg-mul-1 64.3%

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

   9. Simplified 64.3%

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

       1. associate-/r/ 64.3%

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

       2. add-sqr-sqrt 36.1%

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

       3. sqrt-unprod 56.9%

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

       4. sqr-neg 56.9%

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

       5. sqrt-unprod 28.8%

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

       6. add-sqr-sqrt 64.5%

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

   11. Applied egg-rr 64.5%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+86} \lor \neg \left(z \leq 1420000000\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{a}\\ \end{array} \]

Alternative 9: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+174} \lor \neg \left(z \leq 35000000000000\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2e+174) (not (<= z 35000000000000.0)))
   (+ x t)
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e+174) || !(z <= 35000000000000.0)) {
		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 <= (-2d+174)) .or. (.not. (z <= 35000000000000.0d0))) 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 <= -2e+174) || !(z <= 35000000000000.0)) {
		tmp = x + t;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2e+174) or not (z <= 35000000000000.0):
		tmp = x + t
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2e+174) || !(z <= 35000000000000.0))
		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 <= -2e+174) || ~((z <= 35000000000000.0)))
		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, -2e+174], N[Not[LessEqual[z, 35000000000000.0]], $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 < -2.00000000000000014e174 or 3.5e13 < z

   1. Initial program 62.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 86.4%

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

   if -2.00000000000000014e174 < z < 3.5e13

   1. Initial program 92.8%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around 0 75.7%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+174} \lor \neg \left(z \leq 35000000000000\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+174}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+174) (+ x t) (if (<= z 4e+20) (+ x (/ y (/ a t))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+174) {
		tmp = x + t;
	} else if (z <= 4e+20) {
		tmp = x + (y / (a / t));
	} 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 <= (-2d+174)) then
        tmp = x + t
    else if (z <= 4d+20) then
        tmp = x + (y / (a / t))
    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 <= -2e+174) {
		tmp = x + t;
	} else if (z <= 4e+20) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+174:
		tmp = x + t
	elif z <= 4e+20:
		tmp = x + (y / (a / t))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+174)
		tmp = Float64(x + t);
	elseif (z <= 4e+20)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+174)
		tmp = x + t;
	elseif (z <= 4e+20)
		tmp = x + (y / (a / t));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+174], N[(x + t), $MachinePrecision], If[LessEqual[z, 4e+20], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000014e174 or 4e20 < z

   1. Initial program 62.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 86.4%

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

   if -2.00000000000000014e174 < z < 4e20

   1. Initial program 92.8%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around 0 73.9%

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

      1. associate-/l* 77.2%

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

   6. Simplified 77.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+174}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 11: 59.6% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.1%

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

   1. associate-*l/ 98.5%

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

3. Simplified 98.5%

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

4. Taylor expanded in z around inf 59.2%

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

5. Final simplification 59.2%

   \[\leadsto x + t \]

Developer target: 99.3% accurate, 0.7× 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 2023199 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (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))))