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

Percentage Accurate: 85.4% → 98.2%

Time: 11.2s

Alternatives: 14

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: 85.4% 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 86.0%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
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. Final simplification 97.3%

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

Alternative 2: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ t_2 := x - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+91}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))) (t_2 (- x (* t (/ y z)))))
   (if (<= z -1.4e+91)
     (+ x t)
     (if (<= z -2.6e-27)
       t_2
       (if (<= z -1.6e-87)
         t_1
         (if (<= z -5.1e-115)
           t_2
           (if (<= z 1.45e-68)
             t_1
             (if (<= z 1.1e+50)
               t_2
               (if (<= z 1.15e+73) (- x (/ t (/ a z))) (+ x t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double t_2 = x - (t * (y / z));
	double tmp;
	if (z <= -1.4e+91) {
		tmp = x + t;
	} else if (z <= -2.6e-27) {
		tmp = t_2;
	} else if (z <= -1.6e-87) {
		tmp = t_1;
	} else if (z <= -5.1e-115) {
		tmp = t_2;
	} else if (z <= 1.45e-68) {
		tmp = t_1;
	} else if (z <= 1.1e+50) {
		tmp = t_2;
	} else if (z <= 1.15e+73) {
		tmp = x - (t / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    t_2 = x - (t * (y / z))
    if (z <= (-1.4d+91)) then
        tmp = x + t
    else if (z <= (-2.6d-27)) then
        tmp = t_2
    else if (z <= (-1.6d-87)) then
        tmp = t_1
    else if (z <= (-5.1d-115)) then
        tmp = t_2
    else if (z <= 1.45d-68) then
        tmp = t_1
    else if (z <= 1.1d+50) then
        tmp = t_2
    else if (z <= 1.15d+73) then
        tmp = x - (t / (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 t_1 = x + (y / (a / t));
	double t_2 = x - (t * (y / z));
	double tmp;
	if (z <= -1.4e+91) {
		tmp = x + t;
	} else if (z <= -2.6e-27) {
		tmp = t_2;
	} else if (z <= -1.6e-87) {
		tmp = t_1;
	} else if (z <= -5.1e-115) {
		tmp = t_2;
	} else if (z <= 1.45e-68) {
		tmp = t_1;
	} else if (z <= 1.1e+50) {
		tmp = t_2;
	} else if (z <= 1.15e+73) {
		tmp = x - (t / (a / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	t_2 = x - (t * (y / z))
	tmp = 0
	if z <= -1.4e+91:
		tmp = x + t
	elif z <= -2.6e-27:
		tmp = t_2
	elif z <= -1.6e-87:
		tmp = t_1
	elif z <= -5.1e-115:
		tmp = t_2
	elif z <= 1.45e-68:
		tmp = t_1
	elif z <= 1.1e+50:
		tmp = t_2
	elif z <= 1.15e+73:
		tmp = x - (t / (a / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	t_2 = Float64(x - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (z <= -1.4e+91)
		tmp = Float64(x + t);
	elseif (z <= -2.6e-27)
		tmp = t_2;
	elseif (z <= -1.6e-87)
		tmp = t_1;
	elseif (z <= -5.1e-115)
		tmp = t_2;
	elseif (z <= 1.45e-68)
		tmp = t_1;
	elseif (z <= 1.1e+50)
		tmp = t_2;
	elseif (z <= 1.15e+73)
		tmp = Float64(x - Float64(t / Float64(a / z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	t_2 = x - (t * (y / z));
	tmp = 0.0;
	if (z <= -1.4e+91)
		tmp = x + t;
	elseif (z <= -2.6e-27)
		tmp = t_2;
	elseif (z <= -1.6e-87)
		tmp = t_1;
	elseif (z <= -5.1e-115)
		tmp = t_2;
	elseif (z <= 1.45e-68)
		tmp = t_1;
	elseif (z <= 1.1e+50)
		tmp = t_2;
	elseif (z <= 1.15e+73)
		tmp = x - (t / (a / z));
	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[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+91], N[(x + t), $MachinePrecision], If[LessEqual[z, -2.6e-27], t$95$2, If[LessEqual[z, -1.6e-87], t$95$1, If[LessEqual[z, -5.1e-115], t$95$2, If[LessEqual[z, 1.45e-68], t$95$1, If[LessEqual[z, 1.1e+50], t$95$2, If[LessEqual[z, 1.15e+73], N[(x - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3999999999999999e91 or 1.15e73 < z

   1. Initial program 70.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 84.9%

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

   if -1.3999999999999999e91 < z < -2.60000000000000017e-27 or -1.59999999999999989e-87 < z < -5.0999999999999997e-115 or 1.45e-68 < z < 1.10000000000000008e50

   1. Initial program 98.3%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around inf 81.8%

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

   5. Taylor expanded in x around 0 83.1%

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

      1. associate-/l* 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in a around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. associate-*r/ 73.8%

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

      3. *-commutative 73.8%

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

      4. associate-/r/ 74.3%

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

      5. +-commutative 74.3%

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

      6. sub-neg 74.3%

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

      7. associate-/r/ 73.8%

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

      8. associate-*l/ 75.1%

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

      9. associate-*r/ 73.7%

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

   10. Simplified 73.7%

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

   if -2.60000000000000017e-27 < z < -1.59999999999999989e-87 or -5.0999999999999997e-115 < z < 1.45e-68

   1. Initial program 90.9%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around 0 79.7%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a} + x} \]
   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 1.10000000000000008e50 < z < 1.15e73

   1. Initial program 100.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 inf 100.0%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+91}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-27}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-115}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+50}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 3: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ t_2 := x - \frac{y \cdot t}{z}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+94}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-27}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))) (t_2 (- x (/ (* y t) z))))
   (if (<= z -3.1e+94)
     (+ x t)
     (if (<= z -4.2e-27)
       (- x (* t (/ y z)))
       (if (<= z -2.2e-87)
         t_1
         (if (<= z -3.5e-115)
           t_2
           (if (<= z 8.2e-69)
             t_1
             (if (<= z 1.1e+50)
               t_2
               (if (<= z 8.5e+72) (- x (/ t (/ a z))) (+ x t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double t_2 = x - ((y * t) / z);
	double tmp;
	if (z <= -3.1e+94) {
		tmp = x + t;
	} else if (z <= -4.2e-27) {
		tmp = x - (t * (y / z));
	} else if (z <= -2.2e-87) {
		tmp = t_1;
	} else if (z <= -3.5e-115) {
		tmp = t_2;
	} else if (z <= 8.2e-69) {
		tmp = t_1;
	} else if (z <= 1.1e+50) {
		tmp = t_2;
	} else if (z <= 8.5e+72) {
		tmp = x - (t / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    t_2 = x - ((y * t) / z)
    if (z <= (-3.1d+94)) then
        tmp = x + t
    else if (z <= (-4.2d-27)) then
        tmp = x - (t * (y / z))
    else if (z <= (-2.2d-87)) then
        tmp = t_1
    else if (z <= (-3.5d-115)) then
        tmp = t_2
    else if (z <= 8.2d-69) then
        tmp = t_1
    else if (z <= 1.1d+50) then
        tmp = t_2
    else if (z <= 8.5d+72) then
        tmp = x - (t / (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 t_1 = x + (y / (a / t));
	double t_2 = x - ((y * t) / z);
	double tmp;
	if (z <= -3.1e+94) {
		tmp = x + t;
	} else if (z <= -4.2e-27) {
		tmp = x - (t * (y / z));
	} else if (z <= -2.2e-87) {
		tmp = t_1;
	} else if (z <= -3.5e-115) {
		tmp = t_2;
	} else if (z <= 8.2e-69) {
		tmp = t_1;
	} else if (z <= 1.1e+50) {
		tmp = t_2;
	} else if (z <= 8.5e+72) {
		tmp = x - (t / (a / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	t_2 = x - ((y * t) / z)
	tmp = 0
	if z <= -3.1e+94:
		tmp = x + t
	elif z <= -4.2e-27:
		tmp = x - (t * (y / z))
	elif z <= -2.2e-87:
		tmp = t_1
	elif z <= -3.5e-115:
		tmp = t_2
	elif z <= 8.2e-69:
		tmp = t_1
	elif z <= 1.1e+50:
		tmp = t_2
	elif z <= 8.5e+72:
		tmp = x - (t / (a / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	t_2 = Float64(x - Float64(Float64(y * t) / z))
	tmp = 0.0
	if (z <= -3.1e+94)
		tmp = Float64(x + t);
	elseif (z <= -4.2e-27)
		tmp = Float64(x - Float64(t * Float64(y / z)));
	elseif (z <= -2.2e-87)
		tmp = t_1;
	elseif (z <= -3.5e-115)
		tmp = t_2;
	elseif (z <= 8.2e-69)
		tmp = t_1;
	elseif (z <= 1.1e+50)
		tmp = t_2;
	elseif (z <= 8.5e+72)
		tmp = Float64(x - Float64(t / Float64(a / z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	t_2 = x - ((y * t) / z);
	tmp = 0.0;
	if (z <= -3.1e+94)
		tmp = x + t;
	elseif (z <= -4.2e-27)
		tmp = x - (t * (y / z));
	elseif (z <= -2.2e-87)
		tmp = t_1;
	elseif (z <= -3.5e-115)
		tmp = t_2;
	elseif (z <= 8.2e-69)
		tmp = t_1;
	elseif (z <= 1.1e+50)
		tmp = t_2;
	elseif (z <= 8.5e+72)
		tmp = x - (t / (a / z));
	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[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+94], N[(x + t), $MachinePrecision], If[LessEqual[z, -4.2e-27], N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.2e-87], t$95$1, If[LessEqual[z, -3.5e-115], t$95$2, If[LessEqual[z, 8.2e-69], t$95$1, If[LessEqual[z, 1.1e+50], t$95$2, If[LessEqual[z, 8.5e+72], N[(x - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.09999999999999991e94 or 8.5000000000000004e72 < z

   1. Initial program 70.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 84.9%

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

   if -3.09999999999999991e94 < z < -4.20000000000000031e-27

   1. Initial program 96.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 y around inf 82.9%

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

   5. Taylor expanded in x around 0 82.8%

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

      1. associate-/l* 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in a around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. associate-*r/ 79.3%

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

      3. *-commutative 79.3%

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

      4. associate-/r/ 79.1%

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

      5. +-commutative 79.1%

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

      6. sub-neg 79.1%

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

      7. associate-/r/ 79.3%

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

      8. associate-*l/ 79.1%

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

      9. associate-*r/ 79.1%

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

   10. Simplified 79.1%

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

   if -4.20000000000000031e-27 < z < -2.19999999999999988e-87 or -3.5000000000000002e-115 < z < 8.1999999999999998e-69

   1. Initial program 90.9%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around 0 79.7%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a} + x} \]
   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 -2.19999999999999988e-87 < z < -3.5000000000000002e-115 or 8.1999999999999998e-69 < z < 1.10000000000000008e50

   1. Initial program 99.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 y around inf 80.9%

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

   5. Taylor expanded in a around 0 72.0%

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

      1. +-commutative 72.0%

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

      2. mul-1-neg 72.0%

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

      3. unsub-neg 72.0%

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

      4. *-commutative 72.0%

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

   7. Simplified 72.0%

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

   if 1.10000000000000008e50 < z < 8.5000000000000004e72

   1. Initial program 100.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 inf 100.0%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+94}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-27}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-115}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-69}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 4: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ t_2 := x - \frac{y \cdot t}{z}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+90}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+71}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))) (t_2 (- x (/ (* y t) z))))
   (if (<= z -6.8e+90)
     (+ x t)
     (if (<= z -4.8e-27)
       (+ x (/ y (/ (- z) t)))
       (if (<= z -1.6e-87)
         t_1
         (if (<= z -5.1e-115)
           t_2
           (if (<= z 1.9e-68)
             t_1
             (if (<= z 1.1e+50)
               t_2
               (if (<= z 7.5e+71) (- x (/ t (/ a z))) (+ x t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double t_2 = x - ((y * t) / z);
	double tmp;
	if (z <= -6.8e+90) {
		tmp = x + t;
	} else if (z <= -4.8e-27) {
		tmp = x + (y / (-z / t));
	} else if (z <= -1.6e-87) {
		tmp = t_1;
	} else if (z <= -5.1e-115) {
		tmp = t_2;
	} else if (z <= 1.9e-68) {
		tmp = t_1;
	} else if (z <= 1.1e+50) {
		tmp = t_2;
	} else if (z <= 7.5e+71) {
		tmp = x - (t / (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    t_2 = x - ((y * t) / z)
    if (z <= (-6.8d+90)) then
        tmp = x + t
    else if (z <= (-4.8d-27)) then
        tmp = x + (y / (-z / t))
    else if (z <= (-1.6d-87)) then
        tmp = t_1
    else if (z <= (-5.1d-115)) then
        tmp = t_2
    else if (z <= 1.9d-68) then
        tmp = t_1
    else if (z <= 1.1d+50) then
        tmp = t_2
    else if (z <= 7.5d+71) then
        tmp = x - (t / (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 t_1 = x + (y / (a / t));
	double t_2 = x - ((y * t) / z);
	double tmp;
	if (z <= -6.8e+90) {
		tmp = x + t;
	} else if (z <= -4.8e-27) {
		tmp = x + (y / (-z / t));
	} else if (z <= -1.6e-87) {
		tmp = t_1;
	} else if (z <= -5.1e-115) {
		tmp = t_2;
	} else if (z <= 1.9e-68) {
		tmp = t_1;
	} else if (z <= 1.1e+50) {
		tmp = t_2;
	} else if (z <= 7.5e+71) {
		tmp = x - (t / (a / z));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	t_2 = x - ((y * t) / z)
	tmp = 0
	if z <= -6.8e+90:
		tmp = x + t
	elif z <= -4.8e-27:
		tmp = x + (y / (-z / t))
	elif z <= -1.6e-87:
		tmp = t_1
	elif z <= -5.1e-115:
		tmp = t_2
	elif z <= 1.9e-68:
		tmp = t_1
	elif z <= 1.1e+50:
		tmp = t_2
	elif z <= 7.5e+71:
		tmp = x - (t / (a / z))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	t_2 = Float64(x - Float64(Float64(y * t) / z))
	tmp = 0.0
	if (z <= -6.8e+90)
		tmp = Float64(x + t);
	elseif (z <= -4.8e-27)
		tmp = Float64(x + Float64(y / Float64(Float64(-z) / t)));
	elseif (z <= -1.6e-87)
		tmp = t_1;
	elseif (z <= -5.1e-115)
		tmp = t_2;
	elseif (z <= 1.9e-68)
		tmp = t_1;
	elseif (z <= 1.1e+50)
		tmp = t_2;
	elseif (z <= 7.5e+71)
		tmp = Float64(x - Float64(t / Float64(a / z)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	t_2 = x - ((y * t) / z);
	tmp = 0.0;
	if (z <= -6.8e+90)
		tmp = x + t;
	elseif (z <= -4.8e-27)
		tmp = x + (y / (-z / t));
	elseif (z <= -1.6e-87)
		tmp = t_1;
	elseif (z <= -5.1e-115)
		tmp = t_2;
	elseif (z <= 1.9e-68)
		tmp = t_1;
	elseif (z <= 1.1e+50)
		tmp = t_2;
	elseif (z <= 7.5e+71)
		tmp = x - (t / (a / z));
	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[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+90], N[(x + t), $MachinePrecision], If[LessEqual[z, -4.8e-27], N[(x + N[(y / N[((-z) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e-87], t$95$1, If[LessEqual[z, -5.1e-115], t$95$2, If[LessEqual[z, 1.9e-68], t$95$1, If[LessEqual[z, 1.1e+50], t$95$2, If[LessEqual[z, 7.5e+71], N[(x - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.80000000000000036e90 or 7.50000000000000007e71 < z

   1. Initial program 70.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 84.9%

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

   if -6.80000000000000036e90 < z < -4.80000000000000004e-27

   1. Initial program 96.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 y around inf 82.9%

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

   5. Taylor expanded in x around 0 82.8%

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

      1. associate-/l* 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in a around 0 79.1%

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

      1. neg-mul-1 79.1%

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

      2. distribute-neg-frac 79.1%

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

   10. Simplified 79.1%

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

   if -4.80000000000000004e-27 < z < -1.59999999999999989e-87 or -5.0999999999999997e-115 < z < 1.90000000000000019e-68

   1. Initial program 90.9%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around 0 79.7%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a} + x} \]
   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 -1.59999999999999989e-87 < z < -5.0999999999999997e-115 or 1.90000000000000019e-68 < z < 1.10000000000000008e50

   1. Initial program 99.7%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 y around inf 80.9%

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

   5. Taylor expanded in a around 0 72.0%

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

      1. +-commutative 72.0%

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

      2. mul-1-neg 72.0%

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

      3. unsub-neg 72.0%

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

      4. *-commutative 72.0%

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

   7. Simplified 72.0%

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

   if 1.10000000000000008e50 < z < 7.50000000000000007e71

   1. Initial program 100.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 inf 100.0%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. associate-/l* 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+90}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{\frac{-z}{t}}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-115}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{y \cdot t}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+71}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 5: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ t_2 := x - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+90}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))) (t_2 (- x (* t (/ y z)))))
   (if (<= z -7.8e+90)
     (+ x t)
     (if (<= z -3.8e-27)
       t_2
       (if (<= z -4.7e-87)
         t_1
         (if (<= z -2.6e-116)
           t_2
           (if (<= z 1.2e-68)
             t_1
             (if (<= z 1.1e+50) t_2 (if (<= z 7.5e+71) x (+ x t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double t_2 = x - (t * (y / z));
	double tmp;
	if (z <= -7.8e+90) {
		tmp = x + t;
	} else if (z <= -3.8e-27) {
		tmp = t_2;
	} else if (z <= -4.7e-87) {
		tmp = t_1;
	} else if (z <= -2.6e-116) {
		tmp = t_2;
	} else if (z <= 1.2e-68) {
		tmp = t_1;
	} else if (z <= 1.1e+50) {
		tmp = t_2;
	} else if (z <= 7.5e+71) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    t_2 = x - (t * (y / z))
    if (z <= (-7.8d+90)) then
        tmp = x + t
    else if (z <= (-3.8d-27)) then
        tmp = t_2
    else if (z <= (-4.7d-87)) then
        tmp = t_1
    else if (z <= (-2.6d-116)) then
        tmp = t_2
    else if (z <= 1.2d-68) then
        tmp = t_1
    else if (z <= 1.1d+50) then
        tmp = t_2
    else if (z <= 7.5d+71) then
        tmp = x
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double t_2 = x - (t * (y / z));
	double tmp;
	if (z <= -7.8e+90) {
		tmp = x + t;
	} else if (z <= -3.8e-27) {
		tmp = t_2;
	} else if (z <= -4.7e-87) {
		tmp = t_1;
	} else if (z <= -2.6e-116) {
		tmp = t_2;
	} else if (z <= 1.2e-68) {
		tmp = t_1;
	} else if (z <= 1.1e+50) {
		tmp = t_2;
	} else if (z <= 7.5e+71) {
		tmp = x;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	t_2 = x - (t * (y / z))
	tmp = 0
	if z <= -7.8e+90:
		tmp = x + t
	elif z <= -3.8e-27:
		tmp = t_2
	elif z <= -4.7e-87:
		tmp = t_1
	elif z <= -2.6e-116:
		tmp = t_2
	elif z <= 1.2e-68:
		tmp = t_1
	elif z <= 1.1e+50:
		tmp = t_2
	elif z <= 7.5e+71:
		tmp = x
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	t_2 = Float64(x - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (z <= -7.8e+90)
		tmp = Float64(x + t);
	elseif (z <= -3.8e-27)
		tmp = t_2;
	elseif (z <= -4.7e-87)
		tmp = t_1;
	elseif (z <= -2.6e-116)
		tmp = t_2;
	elseif (z <= 1.2e-68)
		tmp = t_1;
	elseif (z <= 1.1e+50)
		tmp = t_2;
	elseif (z <= 7.5e+71)
		tmp = x;
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	t_2 = x - (t * (y / z));
	tmp = 0.0;
	if (z <= -7.8e+90)
		tmp = x + t;
	elseif (z <= -3.8e-27)
		tmp = t_2;
	elseif (z <= -4.7e-87)
		tmp = t_1;
	elseif (z <= -2.6e-116)
		tmp = t_2;
	elseif (z <= 1.2e-68)
		tmp = t_1;
	elseif (z <= 1.1e+50)
		tmp = t_2;
	elseif (z <= 7.5e+71)
		tmp = x;
	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[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+90], N[(x + t), $MachinePrecision], If[LessEqual[z, -3.8e-27], t$95$2, If[LessEqual[z, -4.7e-87], t$95$1, If[LessEqual[z, -2.6e-116], t$95$2, If[LessEqual[z, 1.2e-68], t$95$1, If[LessEqual[z, 1.1e+50], t$95$2, If[LessEqual[z, 7.5e+71], x, N[(x + t), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.8000000000000004e90 or 7.50000000000000007e71 < z

   1. Initial program 70.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 84.9%

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

   if -7.8000000000000004e90 < z < -3.8e-27 or -4.7000000000000001e-87 < z < -2.6e-116 or 1.19999999999999996e-68 < z < 1.10000000000000008e50

   1. Initial program 98.3%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around inf 81.8%

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

   5. Taylor expanded in x around 0 83.1%

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

      1. associate-/l* 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in a around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. associate-*r/ 73.8%

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

      3. *-commutative 73.8%

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

      4. associate-/r/ 74.3%

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

      5. +-commutative 74.3%

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

      6. sub-neg 74.3%

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

      7. associate-/r/ 73.8%

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

      8. associate-*l/ 75.1%

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

      9. associate-*r/ 73.7%

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

   10. Simplified 73.7%

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

   if -3.8e-27 < z < -4.7000000000000001e-87 or -2.6e-116 < z < 1.19999999999999996e-68

   1. Initial program 90.9%

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

      1. associate-*l/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around 0 79.7%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a} + x} \]
   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 1.10000000000000008e50 < z < 7.50000000000000007e71

   1. Initial program 100.0%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 x around inf 75.4%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+90}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-27}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-116}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+50}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 6: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+107} \lor \neg \left(z \leq 6.8 \cdot 10^{+72}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+107) (not (<= z 6.8e+72)))
   (+ x t)
   (+ x (/ y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+107) || !(z <= 6.8e+72)) {
		tmp = x + t;
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.5d+107)) .or. (.not. (z <= 6.8d+72))) then
        tmp = x + t
    else
        tmp = x + (y / ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+107) || !(z <= 6.8e+72)) {
		tmp = x + t;
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e+107) or not (z <= 6.8e+72):
		tmp = x + t
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+107) || !(z <= 6.8e+72))
		tmp = Float64(x + t);
	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 <= -9.5e+107) || ~((z <= 6.8e+72)))
		tmp = x + t;
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+107], N[Not[LessEqual[z, 6.8e+72]], $MachinePrecision]], N[(x + t), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000019e107 or 6.7999999999999997e72 < z

   1. Initial program 70.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 85.5%

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

   if -9.50000000000000019e107 < z < 6.7999999999999997e72

   1. Initial program 93.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 y around inf 86.8%

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

   5. Taylor expanded in x around 0 85.4%

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

      1. associate-/l* 88.7%

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

   7. Simplified 88.7%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+107} \lor \neg \left(z \leq 6.8 \cdot 10^{+72}\right):\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 7: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+108} \lor \neg \left(z \leq 9 \cdot 10^{+49}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.55e+108) (not (<= z 9e+49)))
   (- x (/ t (+ (/ a z) -1.0)))
   (+ x (/ y (/ (- a z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e+108) || !(z <= 9e+49)) {
		tmp = x - (t / ((a / z) + -1.0));
	} 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 <= (-1.55d+108)) .or. (.not. (z <= 9d+49))) then
        tmp = x - (t / ((a / z) + (-1.0d0)))
    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 <= -1.55e+108) || !(z <= 9e+49)) {
		tmp = x - (t / ((a / z) + -1.0));
	} else {
		tmp = x + (y / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.55e+108) or not (z <= 9e+49):
		tmp = x - (t / ((a / z) + -1.0))
	else:
		tmp = x + (y / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.55e+108) || !(z <= 9e+49))
		tmp = Float64(x - Float64(t / Float64(Float64(a / z) + -1.0)));
	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 <= -1.55e+108) || ~((z <= 9e+49)))
		tmp = x - (t / ((a / z) + -1.0));
	else
		tmp = x + (y / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.55e+108], N[Not[LessEqual[z, 9e+49]], $MachinePrecision]], N[(x - N[(t / N[(N[(a / z), $MachinePrecision] + -1.0), $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 < -1.5500000000000001e108 or 8.99999999999999965e49 < z

   1. Initial program 71.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 y around 0 67.9%

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

      1. +-commutative 67.9%

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

      2. mul-1-neg 67.9%

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

      3. *-commutative 67.9%

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

      4. associate-*r/ 89.4%

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

      5. unsub-neg 89.4%

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

      6. associate-*r/ 67.9%

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

      7. *-commutative 67.9%

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

      8. associate-/l* 93.3%

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

      9. div-sub 93.3%

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

      10. *-inverses 93.3%

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

   6. Simplified 93.3%

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

   if -1.5500000000000001e108 < z < 8.99999999999999965e49

   1. Initial program 93.3%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in y around inf 86.9%

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

   5. Taylor expanded in x around 0 85.6%

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

      1. associate-/l* 88.9%

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

   7. Simplified 88.9%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+108} \lor \neg \left(z \leq 9 \cdot 10^{+49}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \end{array} \]

Alternative 8: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+107}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+73}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+107)
   (+ x t)
   (if (<= z 2.35e+73) (+ x (* t (/ y (- a z)))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+107) {
		tmp = x + t;
	} else if (z <= 2.35e+73) {
		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 <= (-3.8d+107)) then
        tmp = x + t
    else if (z <= 2.35d+73) 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 <= -3.8e+107) {
		tmp = x + t;
	} else if (z <= 2.35e+73) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+107:
		tmp = x + t
	elif z <= 2.35e+73:
		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 <= -3.8e+107)
		tmp = Float64(x + t);
	elseif (z <= 2.35e+73)
		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 <= -3.8e+107)
		tmp = x + t;
	elseif (z <= 2.35e+73)
		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, -3.8e+107], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.35e+73], 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 < -3.7999999999999998e107 or 2.3500000000000001e73 < z

   1. Initial program 70.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 85.5%

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

   if -3.7999999999999998e107 < z < 2.3500000000000001e73

   1. Initial program 93.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 y around inf 86.8%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+107}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+73}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 9: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+111}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq 11.5:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+111)
   (- x (/ t (+ (/ a z) -1.0)))
   (if (<= z 11.5) (+ x (/ y (/ (- a z) t))) (- x (/ t (/ z (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+111) {
		tmp = x - (t / ((a / z) + -1.0));
	} else if (z <= 11.5) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x - (t / (z / (y - 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 <= (-1.2d+111)) then
        tmp = x - (t / ((a / z) + (-1.0d0)))
    else if (z <= 11.5d0) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = x - (t / (z / (y - 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 <= -1.2e+111) {
		tmp = x - (t / ((a / z) + -1.0));
	} else if (z <= 11.5) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = x - (t / (z / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+111:
		tmp = x - (t / ((a / z) + -1.0))
	elif z <= 11.5:
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = x - (t / (z / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+111)
		tmp = Float64(x - Float64(t / Float64(Float64(a / z) + -1.0)));
	elseif (z <= 11.5)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x - Float64(t / Float64(z / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e+111)
		tmp = x - (t / ((a / z) + -1.0));
	elseif (z <= 11.5)
		tmp = x + (y / ((a - z) / t));
	else
		tmp = x - (t / (z / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+111], N[(x - N[(t / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 11.5], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.20000000000000003e111

   1. Initial program 67.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 y around 0 64.7%

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

      1. +-commutative 64.7%

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

      2. mul-1-neg 64.7%

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

      3. *-commutative 64.7%

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

      4. associate-*r/ 91.7%

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

      5. unsub-neg 91.7%

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

      6. associate-*r/ 64.7%

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

      7. *-commutative 64.7%

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

      8. associate-/l* 94.4%

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

      9. div-sub 94.4%

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

      10. *-inverses 94.4%

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

   6. Simplified 94.4%

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

   if -1.20000000000000003e111 < z < 11.5

   1. Initial program 92.8%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in y around inf 87.9%

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

   5. Taylor expanded in x around 0 86.5%

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

      1. associate-/l* 90.6%

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

   7. Simplified 90.6%

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

   if 11.5 < z

   1. Initial program 78.2%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 68.4%

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

      1. +-commutative 68.4%

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

      2. mul-1-neg 68.4%

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

      3. unsub-neg 68.4%

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

      4. associate-/l* 89.5%

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

   6. Simplified 89.5%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+111}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq 11.5:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y - z}}\\ \end{array} \]

Alternative 10: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+102}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+71}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.15e+102)
   (+ x t)
   (if (<= z 7.5e+71) (+ x (* t (/ y a))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.15e+102) {
		tmp = x + t;
	} else if (z <= 7.5e+71) {
		tmp = x + (t * (y / a));
	} 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 <= (-2.15d+102)) then
        tmp = x + t
    else if (z <= 7.5d+71) then
        tmp = x + (t * (y / a))
    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 <= -2.15e+102) {
		tmp = x + t;
	} else if (z <= 7.5e+71) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.15e+102:
		tmp = x + t
	elif z <= 7.5e+71:
		tmp = x + (t * (y / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.15e+102)
		tmp = Float64(x + t);
	elseif (z <= 7.5e+71)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.15e+102)
		tmp = x + t;
	elseif (z <= 7.5e+71)
		tmp = x + (t * (y / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.15e+102], N[(x + t), $MachinePrecision], If[LessEqual[z, 7.5e+71], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15e102 or 7.50000000000000007e71 < z

   1. Initial program 70.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 85.7%

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

   if -2.15e102 < z < 7.50000000000000007e71

   1. Initial program 93.3%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around 0 71.7%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+102}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+71}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 11: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+102}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.4:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.15e+102) (+ x t) (if (<= z 7.4) (+ x (* y (/ t a))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.15e+102) {
		tmp = x + t;
	} else if (z <= 7.4) {
		tmp = x + (y * (t / a));
	} 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 <= (-2.15d+102)) then
        tmp = x + t
    else if (z <= 7.4d0) then
        tmp = x + (y * (t / a))
    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 <= -2.15e+102) {
		tmp = x + t;
	} else if (z <= 7.4) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.15e+102:
		tmp = x + t
	elif z <= 7.4:
		tmp = x + (y * (t / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.15e+102)
		tmp = Float64(x + t);
	elseif (z <= 7.4)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.15e+102)
		tmp = x + t;
	elseif (z <= 7.4)
		tmp = x + (y * (t / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.15e+102], N[(x + t), $MachinePrecision], If[LessEqual[z, 7.4], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15e102 or 7.4000000000000004 < z

   1. Initial program 74.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 80.3%

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

   if -2.15e102 < z < 7.4000000000000004

   1. Initial program 92.8%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around inf 87.8%

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

   5. Taylor expanded in x around 0 86.4%

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

      1. associate-/l* 90.5%

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

   7. Simplified 90.5%

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

   8. Taylor expanded in a around inf 70.7%

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

      1. associate-*r/ 75.3%

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

   10. Simplified 75.3%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+102}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.4:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 12: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+102}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 0.7:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.15e+102) (+ x t) (if (<= z 0.7) (+ x (/ y (/ a t))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.15e+102) {
		tmp = x + t;
	} else if (z <= 0.7) {
		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 <= (-2.15d+102)) then
        tmp = x + t
    else if (z <= 0.7d0) 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 <= -2.15e+102) {
		tmp = x + t;
	} else if (z <= 0.7) {
		tmp = x + (y / (a / t));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.15e+102:
		tmp = x + t
	elif z <= 0.7:
		tmp = x + (y / (a / t))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.15e+102)
		tmp = Float64(x + t);
	elseif (z <= 0.7)
		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 <= -2.15e+102)
		tmp = x + t;
	elseif (z <= 0.7)
		tmp = x + (y / (a / t));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.15e+102], N[(x + t), $MachinePrecision], If[LessEqual[z, 0.7], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15e102 or 0.69999999999999996 < z

   1. Initial program 74.5%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 80.3%

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

   if -2.15e102 < z < 0.69999999999999996

   1. Initial program 92.8%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in z around 0 70.7%

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

      1. associate-/l* 75.3%

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

   6. Simplified 75.3%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+102}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 0.7:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

Alternative 13: 63.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+182}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+112}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7e+182) x (if (<= a 2.9e+112) (+ x t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7e+182) {
		tmp = x;
	} else if (a <= 2.9e+112) {
		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 <= (-7d+182)) then
        tmp = x
    else if (a <= 2.9d+112) 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 <= -7e+182) {
		tmp = x;
	} else if (a <= 2.9e+112) {
		tmp = x + t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7e+182:
		tmp = x
	elif a <= 2.9e+112:
		tmp = x + t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7e+182)
		tmp = x;
	elseif (a <= 2.9e+112)
		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 <= -7e+182)
		tmp = x;
	elseif (a <= 2.9e+112)
		tmp = x + t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7e+182], x, If[LessEqual[a, 2.9e+112], N[(x + t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -7.00000000000000045e182 or 2.9000000000000002e112 < a

   1. Initial program 86.8%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 x around inf 72.1%

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

   if -7.00000000000000045e182 < a < 2.9000000000000002e112

   1. Initial program 85.7%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around inf 58.2%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+182}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+112}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 50.7% 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 86.0%

   \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
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 x around inf 49.0%

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

5. Final simplification 49.0%

   \[\leadsto x \]

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 2023196 
(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))))