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

Percentage Accurate: 86.1% → 98.2%

Time: 8.0s

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: 86.1% 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: 98.2% 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 85.6%

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

   1. associate-*l/ 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 2: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+183}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -25000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-66}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4200:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ t (/ z y)))))
   (if (<= z -7e+183)
     (+ x t)
     (if (<= z -25000000000000.0)
       t_1
       (if (<= z 4.8e-66)
         (+ x (/ y (/ a t)))
         (if (<= z 4200.0)
           (- t (* y (/ t z)))
           (if (<= z 1.85e+50)
             (+ x (/ t (/ a y)))
             (if (<= z 5e+123) t_1 (+ x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (z / y));
	double tmp;
	if (z <= -7e+183) {
		tmp = x + t;
	} else if (z <= -25000000000000.0) {
		tmp = t_1;
	} else if (z <= 4.8e-66) {
		tmp = x + (y / (a / t));
	} else if (z <= 4200.0) {
		tmp = t - (y * (t / z));
	} else if (z <= 1.85e+50) {
		tmp = x + (t / (a / y));
	} else if (z <= 5e+123) {
		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 / (z / y))
    if (z <= (-7d+183)) then
        tmp = x + t
    else if (z <= (-25000000000000.0d0)) then
        tmp = t_1
    else if (z <= 4.8d-66) then
        tmp = x + (y / (a / t))
    else if (z <= 4200.0d0) then
        tmp = t - (y * (t / z))
    else if (z <= 1.85d+50) then
        tmp = x + (t / (a / y))
    else if (z <= 5d+123) 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 / (z / y));
	double tmp;
	if (z <= -7e+183) {
		tmp = x + t;
	} else if (z <= -25000000000000.0) {
		tmp = t_1;
	} else if (z <= 4.8e-66) {
		tmp = x + (y / (a / t));
	} else if (z <= 4200.0) {
		tmp = t - (y * (t / z));
	} else if (z <= 1.85e+50) {
		tmp = x + (t / (a / y));
	} else if (z <= 5e+123) {
		tmp = t_1;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t / (z / y))
	tmp = 0
	if z <= -7e+183:
		tmp = x + t
	elif z <= -25000000000000.0:
		tmp = t_1
	elif z <= 4.8e-66:
		tmp = x + (y / (a / t))
	elif z <= 4200.0:
		tmp = t - (y * (t / z))
	elif z <= 1.85e+50:
		tmp = x + (t / (a / y))
	elif z <= 5e+123:
		tmp = t_1
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (z <= -7e+183)
		tmp = Float64(x + t);
	elseif (z <= -25000000000000.0)
		tmp = t_1;
	elseif (z <= 4.8e-66)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 4200.0)
		tmp = Float64(t - Float64(y * Float64(t / z)));
	elseif (z <= 1.85e+50)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 5e+123)
		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 / (z / y));
	tmp = 0.0;
	if (z <= -7e+183)
		tmp = x + t;
	elseif (z <= -25000000000000.0)
		tmp = t_1;
	elseif (z <= 4.8e-66)
		tmp = x + (y / (a / t));
	elseif (z <= 4200.0)
		tmp = t - (y * (t / z));
	elseif (z <= 1.85e+50)
		tmp = x + (t / (a / y));
	elseif (z <= 5e+123)
		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[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+183], N[(x + t), $MachinePrecision], If[LessEqual[z, -25000000000000.0], t$95$1, If[LessEqual[z, 4.8e-66], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4200.0], N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+50], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+123], t$95$1, N[(x + t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.99999999999999974e183 or 4.99999999999999974e123 < z

   1. Initial program 62.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 84.1%

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

   if -6.99999999999999974e183 < z < -2.5e13 or 1.85e50 < z < 4.99999999999999974e123

   1. Initial program 87.3%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 74.1%

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

      1. +-commutative 74.1%

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

      2. mul-1-neg 74.1%

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

      3. unsub-neg 74.1%

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

      4. associate-/l* 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in z around 0 72.3%

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

   if -2.5e13 < z < 4.80000000000000052e-66

   1. Initial program 93.1%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around 0 81.4%

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

      1. associate-/l* 86.0%

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

   6. Simplified 86.0%

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

   if 4.80000000000000052e-66 < z < 4200

   1. Initial program 99.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 90.5%

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

      1. +-commutative 90.5%

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

      2. mul-1-neg 90.5%

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

      3. unsub-neg 90.5%

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

      4. associate-/l* 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in z around 0 90.5%

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

      1. associate-*l/ 90.5%

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

      2. +-commutative 90.5%

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

      3. neg-mul-1 90.5%

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

      4. unsub-neg 90.5%

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

   9. Simplified 90.5%

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

   10. Taylor expanded in x around 0 83.2%

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

       1. associate-*r/ 83.2%

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

   12. Simplified 83.2%

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

   if 4200 < z < 1.85e50

   1. Initial program 89.4%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 0 58.2%

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

      1. *-commutative 58.2%

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

      2. associate-/l* 68.6%

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

   6. Simplified 68.6%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+183}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -25000000000000:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-66}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4200:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+123}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 3: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+90}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4200:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+123}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.1e+90)
   (+ x t)
   (if (<= z 1.8e-65)
     (+ x (/ y (/ a t)))
     (if (<= z 4200.0)
       (- t (* y (/ t z)))
       (if (<= z 9.8e+123) (+ x (/ t (/ a y))) (+ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+90) {
		tmp = x + t;
	} else if (z <= 1.8e-65) {
		tmp = x + (y / (a / t));
	} else if (z <= 4200.0) {
		tmp = t - (y * (t / z));
	} else if (z <= 9.8e+123) {
		tmp = x + (t / (a / y));
	} 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 <= (-3.1d+90)) then
        tmp = x + t
    else if (z <= 1.8d-65) then
        tmp = x + (y / (a / t))
    else if (z <= 4200.0d0) then
        tmp = t - (y * (t / z))
    else if (z <= 9.8d+123) then
        tmp = x + (t / (a / y))
    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 <= -3.1e+90) {
		tmp = x + t;
	} else if (z <= 1.8e-65) {
		tmp = x + (y / (a / t));
	} else if (z <= 4200.0) {
		tmp = t - (y * (t / z));
	} else if (z <= 9.8e+123) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.1e+90:
		tmp = x + t
	elif z <= 1.8e-65:
		tmp = x + (y / (a / t))
	elif z <= 4200.0:
		tmp = t - (y * (t / z))
	elif z <= 9.8e+123:
		tmp = x + (t / (a / y))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.1e+90)
		tmp = Float64(x + t);
	elseif (z <= 1.8e-65)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= 4200.0)
		tmp = Float64(t - Float64(y * Float64(t / z)));
	elseif (z <= 9.8e+123)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.1e+90)
		tmp = x + t;
	elseif (z <= 1.8e-65)
		tmp = x + (y / (a / t));
	elseif (z <= 4200.0)
		tmp = t - (y * (t / z));
	elseif (z <= 9.8e+123)
		tmp = x + (t / (a / y));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.1e+90], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.8e-65], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4200.0], N[(t - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+123], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.09999999999999988e90 or 9.79999999999999952e123 < z

   1. Initial program 69.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 77.2%

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

   if -3.09999999999999988e90 < z < 1.7999999999999999e-65

   1. Initial program 92.7%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in z around 0 77.3%

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

      1. associate-/l* 81.2%

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

   6. Simplified 81.2%

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

   if 1.7999999999999999e-65 < z < 4200

   1. Initial program 99.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 90.5%

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

      1. +-commutative 90.5%

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

      2. mul-1-neg 90.5%

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

      3. unsub-neg 90.5%

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

      4. associate-/l* 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in z around 0 90.5%

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

      1. associate-*l/ 90.5%

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

      2. +-commutative 90.5%

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

      3. neg-mul-1 90.5%

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

      4. unsub-neg 90.5%

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

   9. Simplified 90.5%

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

   10. Taylor expanded in x around 0 83.2%

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

       1. associate-*r/ 83.2%

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

   12. Simplified 83.2%

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

   if 4200 < z < 9.79999999999999952e123

   1. Initial program 91.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 0 58.3%

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

      1. *-commutative 58.3%

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

      2. associate-/l* 66.5%

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

   6. Simplified 66.5%

      \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}} + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+90}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 4200:\\ \;\;\;\;t - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+123}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 4: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+110} \lor \neg \left(z \leq 2.5 \cdot 10^{-86}\right):\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e+110) (not (<= z 2.5e-86)))
   (+ x (- t (* t (/ y z))))
   (+ x (* t (/ y (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e+110) || !(z <= 2.5e-86)) {
		tmp = x + (t - (t * (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 <= (-1.7d+110)) .or. (.not. (z <= 2.5d-86))) then
        tmp = x + (t - (t * (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 <= -1.7e+110) || !(z <= 2.5e-86)) {
		tmp = x + (t - (t * (y / z)));
	} else {
		tmp = x + (t * (y / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.7e+110) or not (z <= 2.5e-86):
		tmp = x + (t - (t * (y / z)))
	else:
		tmp = x + (t * (y / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.7e+110) || !(z <= 2.5e-86))
		tmp = Float64(x + Float64(t - Float64(t * 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 <= -1.7e+110) || ~((z <= 2.5e-86)))
		tmp = x + (t - (t * (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, -1.7e+110], N[Not[LessEqual[z, 2.5e-86]], $MachinePrecision]], N[(x + N[(t - N[(t * 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 < -1.7000000000000001e110 or 2.4999999999999999e-86 < z

   1. Initial program 78.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 a around 0 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. associate-/l* 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in z around 0 83.6%

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

      1. associate-*l/ 90.4%

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

      2. +-commutative 90.4%

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

      3. neg-mul-1 90.4%

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

      4. unsub-neg 90.4%

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

   9. Simplified 90.4%

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

   if -1.7000000000000001e110 < z < 2.4999999999999999e-86

   1. Initial program 91.4%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in y around inf 88.0%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+110} \lor \neg \left(z \leq 2.5 \cdot 10^{-86}\right):\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 5: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3600000000 \lor \neg \left(y \leq 3.2 \cdot 10^{-120}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3600000000.0) (not (<= y 3.2e-120)))
   (+ x (* t (/ y (- a z))))
   (- x (/ t (+ (/ a z) -1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3600000000.0) || !(y <= 3.2e-120)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (t / ((a / z) + -1.0));
	}
	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 <= (-3600000000.0d0)) .or. (.not. (y <= 3.2d-120))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x - (t / ((a / z) + (-1.0d0)))
    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 <= -3600000000.0) || !(y <= 3.2e-120)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x - (t / ((a / z) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3600000000.0) or not (y <= 3.2e-120):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x - (t / ((a / z) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3600000000.0) || !(y <= 3.2e-120))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x - Float64(t / Float64(Float64(a / z) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3600000000.0) || ~((y <= 3.2e-120)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x - (t / ((a / z) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3600000000.0], N[Not[LessEqual[y, 3.2e-120]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e9 or 3.1999999999999999e-120 < y

   1. Initial program 82.7%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in y around inf 86.2%

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

   if -3.6e9 < y < 3.1999999999999999e-120

   1. Initial program 90.4%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 0 84.4%

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

      1. +-commutative 84.4%

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

      2. mul-1-neg 84.4%

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

      3. unsub-neg 84.4%

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

      4. associate-/l* 93.9%

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

      5. div-sub 93.9%

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

      6. *-inverses 93.9%

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

   6. Simplified 93.9%

      \[\leadsto \color{blue}{x - \frac{t}{\frac{a}{z} - 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3600000000 \lor \neg \left(y \leq 3.2 \cdot 10^{-120}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \end{array} \]

Alternative 6: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+184}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+124}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+184)
   (+ x t)
   (if (<= z 1.52e+124) (+ x (* t (/ y (- a z)))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+184) {
		tmp = x + t;
	} else if (z <= 1.52e+124) {
		tmp = x + (t * (y / (a - z)));
	} 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 <= (-2.7d+184)) then
        tmp = x + t
    else if (z <= 1.52d+124) then
        tmp = x + (t * (y / (a - z)))
    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 <= -2.7e+184) {
		tmp = x + t;
	} else if (z <= 1.52e+124) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+184:
		tmp = x + t
	elif z <= 1.52e+124:
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e+184)
		tmp = Float64(x + t);
	elseif (z <= 1.52e+124)
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.7e+184)
		tmp = x + t;
	elseif (z <= 1.52e+124)
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e+184], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.52e+124], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999999e184 or 1.51999999999999998e124 < z

   1. Initial program 63.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 85.6%

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

   if -2.6999999999999999e184 < z < 1.51999999999999998e124

   1. Initial program 91.3%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in y around inf 84.9%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+184}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{+124}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 7: 58.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-159}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+197}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.02e-159)
   (+ x t)
   (if (<= t 7.2e+52) x (if (<= t 9e+197) (+ x t) (* (/ t z) (- y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.02e-159) {
		tmp = x + t;
	} else if (t <= 7.2e+52) {
		tmp = x;
	} else if (t <= 9e+197) {
		tmp = x + t;
	} else {
		tmp = (t / z) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.02d-159)) then
        tmp = x + t
    else if (t <= 7.2d+52) then
        tmp = x
    else if (t <= 9d+197) then
        tmp = x + t
    else
        tmp = (t / z) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.02e-159) {
		tmp = x + t;
	} else if (t <= 7.2e+52) {
		tmp = x;
	} else if (t <= 9e+197) {
		tmp = x + t;
	} else {
		tmp = (t / z) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.02e-159:
		tmp = x + t
	elif t <= 7.2e+52:
		tmp = x
	elif t <= 9e+197:
		tmp = x + t
	else:
		tmp = (t / z) * -y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.02e-159)
		tmp = Float64(x + t);
	elseif (t <= 7.2e+52)
		tmp = x;
	elseif (t <= 9e+197)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(t / z) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.02e-159)
		tmp = x + t;
	elseif (t <= 7.2e+52)
		tmp = x;
	elseif (t <= 9e+197)
		tmp = x + t;
	else
		tmp = (t / z) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.02e-159], N[(x + t), $MachinePrecision], If[LessEqual[t, 7.2e+52], x, If[LessEqual[t, 9e+197], N[(x + t), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.02e-159 or 7.2e52 < t < 9.0000000000000006e197

   1. Initial program 75.3%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around inf 54.9%

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

   if -1.02e-159 < t < 7.2e52

   1. Initial program 99.0%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in x around inf 75.2%

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

   if 9.0000000000000006e197 < t

   1. Initial program 84.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

      4. associate-/l* 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in z around 0 62.7%

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

      1. associate-*l/ 62.9%

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

      2. +-commutative 62.9%

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

      3. neg-mul-1 62.9%

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

      4. unsub-neg 62.9%

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

   9. Simplified 62.9%

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

   10. Taylor expanded in y around inf 56.5%

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

       1. mul-1-neg 56.5%

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

       2. associate-*r/ 56.8%

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

       3. distribute-rgt-neg-in 56.8%

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

       4. distribute-neg-frac 56.8%

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

   12. Simplified 56.8%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-159}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+197}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \end{array} \]

Alternative 8: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+91} \lor \neg \left(z \leq 1.22 \cdot 10^{+124}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e+91) (not (<= z 1.22e+124))) (+ x t) (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+91) || !(z <= 1.22e+124)) {
		tmp = x + t;
	} else {
		tmp = x + (t / (a / y));
	}
	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 <= (-1.3d+91)) .or. (.not. (z <= 1.22d+124))) then
        tmp = x + t
    else
        tmp = x + (t / (a / y))
    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 <= -1.3e+91) || !(z <= 1.22e+124)) {
		tmp = x + t;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.3e+91) or not (z <= 1.22e+124):
		tmp = x + t
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.3e+91) || !(z <= 1.22e+124))
		tmp = Float64(x + t);
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.3e+91) || ~((z <= 1.22e+124)))
		tmp = x + t;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.3e+91], N[Not[LessEqual[z, 1.22e+124]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e91 or 1.22e124 < z

   1. Initial program 68.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 78.0%

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

   if -1.3e91 < z < 1.22e124

   1. Initial program 93.1%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around 0 71.0%

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

      1. *-commutative 71.0%

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

      2. associate-/l* 74.1%

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

   6. Simplified 74.1%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+91} \lor \neg \left(z \leq 1.22 \cdot 10^{+124}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 9: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+91}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+124}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+91)
   (+ x t)
   (if (<= z 1.06e+124) (+ x (/ y (/ a t))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+91) {
		tmp = x + t;
	} else if (z <= 1.06e+124) {
		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 <= (-1.45d+91)) then
        tmp = x + t
    else if (z <= 1.06d+124) 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 <= -1.45e+91) {
		tmp = x + t;
	} else if (z <= 1.06e+124) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+91:
		tmp = x + t
	elif z <= 1.06e+124:
		tmp = x + (y / (a / t))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+91)
		tmp = Float64(x + t);
	elseif (z <= 1.06e+124)
		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 <= -1.45e+91)
		tmp = x + t;
	elseif (z <= 1.06e+124)
		tmp = x + (y / (a / t));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+91], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.06e+124], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45000000000000007e91 or 1.06e124 < z

   1. Initial program 68.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 78.0%

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

   if -1.45000000000000007e91 < z < 1.06e124

   1. Initial program 93.1%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around 0 71.0%

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

      1. associate-/l* 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+91}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+124}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 10: 62.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 3.2 \cdot 10^{+149}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 3.2e+149) (+ x t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 3.2e+149) {
		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 (a <= 3.2d+149) 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 (a <= 3.2e+149) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 3.2e+149:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 3.2e+149)
		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 (a <= 3.2e+149)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 3.2e+149], N[(x + t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 3.2000000000000002e149

   1. Initial program 86.9%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in z around inf 57.5%

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

   if 3.2000000000000002e149 < a

   1. Initial program 76.7%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 64.1%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.2 \cdot 10^{+149}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 51.6% 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 85.6%

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

   1. associate-*l/ 98.0%

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

3. Simplified 98.0%

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

4. Taylor expanded in x around inf 47.1%

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

5. Final simplification 47.1%

   \[\leadsto x \]

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 2023268 
(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))))