Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Percentage Accurate: 97.0% → 99.6%

Time: 11.3s

Alternatives: 16

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

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

Initial Program: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) + 1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) + 1.0) / a));
end

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + a \cdot \frac{z - y}{\left(t - z\right) + 1} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* a (/ (- z y) (+ (- t z) 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (a * ((z - y) / ((t - z) + 1.0)));
}

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 + (a * ((z - y) / ((t - z) + 1.0d0)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (a * ((z - y) / ((t - z) + 1.0)));
}

Python

def code(x, y, z, t, a):
	return x + (a * ((z - y) / ((t - z) + 1.0)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(a * Float64(Float64(z - y) / Float64(Float64(t - z) + 1.0))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (a * ((z - y) / ((t - z) + 1.0)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.2%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Step-by-step derivation

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 72.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+16}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-177}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-257}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+132}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -4.4e+16)
     (- x a)
     (if (<= z -1.95e-177)
       (- x (* a (/ y t)))
       (if (<= z -7.5e-278)
         t_1
         (if (<= z 3.05e-257)
           (- x (* y (/ a t)))
           (if (<= z 2.55e-16)
             t_1
             (if (<= z 3.1e+132) (+ x (* y (/ a z))) (- x a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -4.4e+16) {
		tmp = x - a;
	} else if (z <= -1.95e-177) {
		tmp = x - (a * (y / t));
	} else if (z <= -7.5e-278) {
		tmp = t_1;
	} else if (z <= 3.05e-257) {
		tmp = x - (y * (a / t));
	} else if (z <= 2.55e-16) {
		tmp = t_1;
	} else if (z <= 3.1e+132) {
		tmp = x + (y * (a / z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * a)
    if (z <= (-4.4d+16)) then
        tmp = x - a
    else if (z <= (-1.95d-177)) then
        tmp = x - (a * (y / t))
    else if (z <= (-7.5d-278)) then
        tmp = t_1
    else if (z <= 3.05d-257) then
        tmp = x - (y * (a / t))
    else if (z <= 2.55d-16) then
        tmp = t_1
    else if (z <= 3.1d+132) then
        tmp = x + (y * (a / z))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -4.4e+16) {
		tmp = x - a;
	} else if (z <= -1.95e-177) {
		tmp = x - (a * (y / t));
	} else if (z <= -7.5e-278) {
		tmp = t_1;
	} else if (z <= 3.05e-257) {
		tmp = x - (y * (a / t));
	} else if (z <= 2.55e-16) {
		tmp = t_1;
	} else if (z <= 3.1e+132) {
		tmp = x + (y * (a / z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	tmp = 0
	if z <= -4.4e+16:
		tmp = x - a
	elif z <= -1.95e-177:
		tmp = x - (a * (y / t))
	elif z <= -7.5e-278:
		tmp = t_1
	elif z <= 3.05e-257:
		tmp = x - (y * (a / t))
	elif z <= 2.55e-16:
		tmp = t_1
	elif z <= 3.1e+132:
		tmp = x + (y * (a / z))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (z <= -4.4e+16)
		tmp = Float64(x - a);
	elseif (z <= -1.95e-177)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= -7.5e-278)
		tmp = t_1;
	elseif (z <= 3.05e-257)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	elseif (z <= 2.55e-16)
		tmp = t_1;
	elseif (z <= 3.1e+132)
		tmp = Float64(x + Float64(y * Float64(a / z)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	tmp = 0.0;
	if (z <= -4.4e+16)
		tmp = x - a;
	elseif (z <= -1.95e-177)
		tmp = x - (a * (y / t));
	elseif (z <= -7.5e-278)
		tmp = t_1;
	elseif (z <= 3.05e-257)
		tmp = x - (y * (a / t));
	elseif (z <= 2.55e-16)
		tmp = t_1;
	elseif (z <= 3.1e+132)
		tmp = x + (y * (a / z));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+16], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.95e-177], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-278], t$95$1, If[LessEqual[z, 3.05e-257], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.55e-16], t$95$1, If[LessEqual[z, 3.1e+132], N[(x + N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.4e16 or 3.0999999999999998e132 < z

   1. Initial program 93.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 79.4%

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

   if -4.4e16 < z < -1.95000000000000007e-177

   1. Initial program 95.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 80.2%

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

   5. Taylor expanded in y around inf 75.5%

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

   if -1.95000000000000007e-177 < z < -7.49999999999999946e-278 or 3.0499999999999998e-257 < z < 2.55e-16

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 81.4%

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

   5. Taylor expanded in z around 0 79.9%

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

   if -7.49999999999999946e-278 < z < 3.0499999999999998e-257

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 77.0%

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

   5. Taylor expanded in y around inf 82.5%

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

      1. associate-*r/ 82.4%

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

   7. Simplified 82.4%

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

   if 2.55e-16 < z < 3.0999999999999998e132

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 86.6%

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

   5. Taylor expanded in z around inf 71.6%

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

      1. associate-/l* 74.8%

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

   7. Simplified 74.8%

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

      1. associate-/r/ 74.9%

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

   9. Applied egg-rr 74.9%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+16}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-177}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-278}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-257}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+132}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 3: 72.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -3.35 \cdot 10^{+19}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-177}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-257}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+126}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -3.35e+19)
     (- x a)
     (if (<= z -1.95e-177)
       (- x (* a (/ y t)))
       (if (<= z -1.85e-277)
         t_1
         (if (<= z 2.8e-257)
           (- x (/ y (/ t a)))
           (if (<= z 2.5e-16)
             t_1
             (if (<= z 3.2e+126) (+ x (* y (/ a z))) (- x a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -3.35e+19) {
		tmp = x - a;
	} else if (z <= -1.95e-177) {
		tmp = x - (a * (y / t));
	} else if (z <= -1.85e-277) {
		tmp = t_1;
	} else if (z <= 2.8e-257) {
		tmp = x - (y / (t / a));
	} else if (z <= 2.5e-16) {
		tmp = t_1;
	} else if (z <= 3.2e+126) {
		tmp = x + (y * (a / z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * a)
    if (z <= (-3.35d+19)) then
        tmp = x - a
    else if (z <= (-1.95d-177)) then
        tmp = x - (a * (y / t))
    else if (z <= (-1.85d-277)) then
        tmp = t_1
    else if (z <= 2.8d-257) then
        tmp = x - (y / (t / a))
    else if (z <= 2.5d-16) then
        tmp = t_1
    else if (z <= 3.2d+126) then
        tmp = x + (y * (a / z))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -3.35e+19) {
		tmp = x - a;
	} else if (z <= -1.95e-177) {
		tmp = x - (a * (y / t));
	} else if (z <= -1.85e-277) {
		tmp = t_1;
	} else if (z <= 2.8e-257) {
		tmp = x - (y / (t / a));
	} else if (z <= 2.5e-16) {
		tmp = t_1;
	} else if (z <= 3.2e+126) {
		tmp = x + (y * (a / z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	tmp = 0
	if z <= -3.35e+19:
		tmp = x - a
	elif z <= -1.95e-177:
		tmp = x - (a * (y / t))
	elif z <= -1.85e-277:
		tmp = t_1
	elif z <= 2.8e-257:
		tmp = x - (y / (t / a))
	elif z <= 2.5e-16:
		tmp = t_1
	elif z <= 3.2e+126:
		tmp = x + (y * (a / z))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (z <= -3.35e+19)
		tmp = Float64(x - a);
	elseif (z <= -1.95e-177)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= -1.85e-277)
		tmp = t_1;
	elseif (z <= 2.8e-257)
		tmp = Float64(x - Float64(y / Float64(t / a)));
	elseif (z <= 2.5e-16)
		tmp = t_1;
	elseif (z <= 3.2e+126)
		tmp = Float64(x + Float64(y * Float64(a / z)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	tmp = 0.0;
	if (z <= -3.35e+19)
		tmp = x - a;
	elseif (z <= -1.95e-177)
		tmp = x - (a * (y / t));
	elseif (z <= -1.85e-277)
		tmp = t_1;
	elseif (z <= 2.8e-257)
		tmp = x - (y / (t / a));
	elseif (z <= 2.5e-16)
		tmp = t_1;
	elseif (z <= 3.2e+126)
		tmp = x + (y * (a / z));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.35e+19], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.95e-177], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.85e-277], t$95$1, If[LessEqual[z, 2.8e-257], N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-16], t$95$1, If[LessEqual[z, 3.2e+126], N[(x + N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.35e19 or 3.1999999999999998e126 < z

   1. Initial program 93.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 79.4%

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

   if -3.35e19 < z < -1.95000000000000007e-177

   1. Initial program 95.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 80.2%

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

   5. Taylor expanded in y around inf 75.5%

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

   if -1.95000000000000007e-177 < z < -1.84999999999999992e-277 or 2.80000000000000001e-257 < z < 2.5000000000000002e-16

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 81.4%

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

   5. Taylor expanded in z around 0 79.9%

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

   if -1.84999999999999992e-277 < z < 2.80000000000000001e-257

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 77.0%

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

   5. Taylor expanded in y around inf 82.5%

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

      1. associate-*r/ 82.4%

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

   7. Simplified 82.4%

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

      1. clear-num 82.4%

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

      2. un-div-inv 82.6%

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

   9. Applied egg-rr 82.6%

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

   if 2.5000000000000002e-16 < z < 3.1999999999999998e126

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 86.6%

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

   5. Taylor expanded in z around inf 71.6%

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

      1. associate-/l* 74.8%

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

   7. Simplified 74.8%

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

      1. associate-/r/ 74.9%

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

   9. Applied egg-rr 74.9%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{+19}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-177}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-277}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-257}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+126}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 4: 71.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -17000000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-177}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-257}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -17000000000000.0)
     (- x a)
     (if (<= z -2e-177)
       (- x (* a (/ y t)))
       (if (<= z -4.5e-278)
         t_1
         (if (<= z 5.9e-257)
           (- x (/ y (/ t a)))
           (if (<= z 3e-143) t_1 (+ x (/ a (/ (- 1.0 z) z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -17000000000000.0) {
		tmp = x - a;
	} else if (z <= -2e-177) {
		tmp = x - (a * (y / t));
	} else if (z <= -4.5e-278) {
		tmp = t_1;
	} else if (z <= 5.9e-257) {
		tmp = x - (y / (t / a));
	} else if (z <= 3e-143) {
		tmp = t_1;
	} else {
		tmp = x + (a / ((1.0 - z) / 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) :: t_1
    real(8) :: tmp
    t_1 = x - (y * a)
    if (z <= (-17000000000000.0d0)) then
        tmp = x - a
    else if (z <= (-2d-177)) then
        tmp = x - (a * (y / t))
    else if (z <= (-4.5d-278)) then
        tmp = t_1
    else if (z <= 5.9d-257) then
        tmp = x - (y / (t / a))
    else if (z <= 3d-143) then
        tmp = t_1
    else
        tmp = x + (a / ((1.0d0 - z) / z))
    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);
	double tmp;
	if (z <= -17000000000000.0) {
		tmp = x - a;
	} else if (z <= -2e-177) {
		tmp = x - (a * (y / t));
	} else if (z <= -4.5e-278) {
		tmp = t_1;
	} else if (z <= 5.9e-257) {
		tmp = x - (y / (t / a));
	} else if (z <= 3e-143) {
		tmp = t_1;
	} else {
		tmp = x + (a / ((1.0 - z) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	tmp = 0
	if z <= -17000000000000.0:
		tmp = x - a
	elif z <= -2e-177:
		tmp = x - (a * (y / t))
	elif z <= -4.5e-278:
		tmp = t_1
	elif z <= 5.9e-257:
		tmp = x - (y / (t / a))
	elif z <= 3e-143:
		tmp = t_1
	else:
		tmp = x + (a / ((1.0 - z) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (z <= -17000000000000.0)
		tmp = Float64(x - a);
	elseif (z <= -2e-177)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= -4.5e-278)
		tmp = t_1;
	elseif (z <= 5.9e-257)
		tmp = Float64(x - Float64(y / Float64(t / a)));
	elseif (z <= 3e-143)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 - z) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	tmp = 0.0;
	if (z <= -17000000000000.0)
		tmp = x - a;
	elseif (z <= -2e-177)
		tmp = x - (a * (y / t));
	elseif (z <= -4.5e-278)
		tmp = t_1;
	elseif (z <= 5.9e-257)
		tmp = x - (y / (t / a));
	elseif (z <= 3e-143)
		tmp = t_1;
	else
		tmp = x + (a / ((1.0 - z) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -17000000000000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, -2e-177], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.5e-278], t$95$1, If[LessEqual[z, 5.9e-257], N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-143], t$95$1, N[(x + N[(a / N[(N[(1.0 - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.7e13

   1. Initial program 94.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 75.3%

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

   if -1.7e13 < z < -1.9999999999999999e-177

   1. Initial program 95.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 80.2%

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

   5. Taylor expanded in y around inf 75.5%

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

   if -1.9999999999999999e-177 < z < -4.4999999999999998e-278 or 5.9e-257 < z < 2.99999999999999985e-143

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 88.5%

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

   5. Taylor expanded in z around 0 88.5%

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

   if -4.4999999999999998e-278 < z < 5.9e-257

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 77.0%

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

   5. Taylor expanded in y around inf 82.5%

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

      1. associate-*r/ 82.4%

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

   7. Simplified 82.4%

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

      1. clear-num 82.4%

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

      2. un-div-inv 82.6%

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

   9. Applied egg-rr 82.6%

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

   if 2.99999999999999985e-143 < z

   1. Initial program 95.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. neg-mul-1 83.3%

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

      3. associate--l+ 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in t around 0 60.5%

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

      1. sub-neg 60.5%

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

      2. mul-1-neg 60.5%

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

      3. remove-double-neg 60.5%

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

      4. associate-/l* 74.2%

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

   9. Simplified 74.2%

      \[\leadsto \color{blue}{x + \frac{a}{\frac{1 - z}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -17000000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-177}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-278}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-257}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-143}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \end{array} \]

Alternative 5: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-19}:\\ \;\;\;\;x - \frac{y - z}{\frac{t + 1}{a}}\\ \mathbf{elif}\;z \leq 10^{+32}:\\ \;\;\;\;x + \frac{a \cdot \left(z - y\right)}{1 - z}\\ \mathbf{elif}\;z \leq 10^{+66}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z y) (/ (- z) a)))))
   (if (<= z -8.5e+31)
     t_1
     (if (<= z 3.9e-19)
       (- x (/ (- y z) (/ (+ t 1.0) a)))
       (if (<= z 1e+32)
         (+ x (/ (* a (- z y)) (- 1.0 z)))
         (if (<= z 1e+66) (+ x (/ (- z y) (/ t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) / (-z / a));
	double tmp;
	if (z <= -8.5e+31) {
		tmp = t_1;
	} else if (z <= 3.9e-19) {
		tmp = x - ((y - z) / ((t + 1.0) / a));
	} else if (z <= 1e+32) {
		tmp = x + ((a * (z - y)) / (1.0 - z));
	} else if (z <= 1e+66) {
		tmp = x + ((z - y) / (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - y) / (-z / a))
    if (z <= (-8.5d+31)) then
        tmp = t_1
    else if (z <= 3.9d-19) then
        tmp = x - ((y - z) / ((t + 1.0d0) / a))
    else if (z <= 1d+32) then
        tmp = x + ((a * (z - y)) / (1.0d0 - z))
    else if (z <= 1d+66) then
        tmp = x + ((z - y) / (t / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) / (-z / a));
	double tmp;
	if (z <= -8.5e+31) {
		tmp = t_1;
	} else if (z <= 3.9e-19) {
		tmp = x - ((y - z) / ((t + 1.0) / a));
	} else if (z <= 1e+32) {
		tmp = x + ((a * (z - y)) / (1.0 - z));
	} else if (z <= 1e+66) {
		tmp = x + ((z - y) / (t / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) / (-z / a))
	tmp = 0
	if z <= -8.5e+31:
		tmp = t_1
	elif z <= 3.9e-19:
		tmp = x - ((y - z) / ((t + 1.0) / a))
	elif z <= 1e+32:
		tmp = x + ((a * (z - y)) / (1.0 - z))
	elif z <= 1e+66:
		tmp = x + ((z - y) / (t / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) / Float64(Float64(-z) / a)))
	tmp = 0.0
	if (z <= -8.5e+31)
		tmp = t_1;
	elseif (z <= 3.9e-19)
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(t + 1.0) / a)));
	elseif (z <= 1e+32)
		tmp = Float64(x + Float64(Float64(a * Float64(z - y)) / Float64(1.0 - z)));
	elseif (z <= 1e+66)
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) / (-z / a));
	tmp = 0.0;
	if (z <= -8.5e+31)
		tmp = t_1;
	elseif (z <= 3.9e-19)
		tmp = x - ((y - z) / ((t + 1.0) / a));
	elseif (z <= 1e+32)
		tmp = x + ((a * (z - y)) / (1.0 - z));
	elseif (z <= 1e+66)
		tmp = x + ((z - y) / (t / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+31], t$95$1, If[LessEqual[z, 3.9e-19], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(t + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+32], N[(x + N[(N[(a * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+66], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.49999999999999947e31 or 9.99999999999999945e65 < z

   1. Initial program 93.6%

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

   2. Taylor expanded in z around inf 84.3%

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

      1. mul-1-neg 84.3%

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

      2. distribute-neg-frac 84.3%

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

   4. Simplified 84.3%

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

   if -8.49999999999999947e31 < z < 3.89999999999999995e-19

   1. Initial program 98.2%

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

   2. Taylor expanded in z around 0 98.2%

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

   if 3.89999999999999995e-19 < z < 1.00000000000000005e32

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 100.0%

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

   if 1.00000000000000005e32 < z < 9.99999999999999945e65

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 75.3%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-19}:\\ \;\;\;\;x - \frac{y - z}{\frac{t + 1}{a}}\\ \mathbf{elif}\;z \leq 10^{+32}:\\ \;\;\;\;x + \frac{a \cdot \left(z - y\right)}{1 - z}\\ \mathbf{elif}\;z \leq 10^{+66}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \end{array} \]

Alternative 6: 84.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+32}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-34}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+130}:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+32)
   (- x a)
   (if (<= z 1.25e-34)
     (- x (/ a (/ (+ t 1.0) y)))
     (if (<= z 8.5e+130) (- x (/ a (/ (- 1.0 z) y))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+32) {
		tmp = x - a;
	} else if (z <= 1.25e-34) {
		tmp = x - (a / ((t + 1.0) / y));
	} else if (z <= 8.5e+130) {
		tmp = x - (a / ((1.0 - z) / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.2d+32)) then
        tmp = x - a
    else if (z <= 1.25d-34) then
        tmp = x - (a / ((t + 1.0d0) / y))
    else if (z <= 8.5d+130) then
        tmp = x - (a / ((1.0d0 - z) / y))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+32) {
		tmp = x - a;
	} else if (z <= 1.25e-34) {
		tmp = x - (a / ((t + 1.0) / y));
	} else if (z <= 8.5e+130) {
		tmp = x - (a / ((1.0 - z) / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+32:
		tmp = x - a
	elif z <= 1.25e-34:
		tmp = x - (a / ((t + 1.0) / y))
	elif z <= 8.5e+130:
		tmp = x - (a / ((1.0 - z) / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+32)
		tmp = Float64(x - a);
	elseif (z <= 1.25e-34)
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	elseif (z <= 8.5e+130)
		tmp = Float64(x - Float64(a / Float64(Float64(1.0 - z) / y)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e+32)
		tmp = x - a;
	elseif (z <= 1.25e-34)
		tmp = x - (a / ((t + 1.0) / y));
	elseif (z <= 8.5e+130)
		tmp = x - (a / ((1.0 - z) / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+32], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.25e-34], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+130], N[(x - N[(a / N[(N[(1.0 - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2000000000000004e32 or 8.49999999999999965e130 < z

   1. Initial program 93.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.0%

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

   if -5.2000000000000004e32 < z < 1.2500000000000001e-34

   1. Initial program 98.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*l/ 92.4%

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

   5. Applied egg-rr 92.4%

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

   6. Taylor expanded in z around 0 83.8%

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

      1. associate-/l* 91.2%

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

   8. Simplified 91.2%

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

   if 1.2500000000000001e-34 < z < 8.49999999999999965e130

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 79.2%

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

   5. Taylor expanded in y around inf 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-/l* 79.0%

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

   7. Simplified 79.0%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+32}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-34}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+130}:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 7: 87.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+32} \lor \neg \left(z \leq 1.28 \cdot 10^{+112}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+32) (not (<= z 1.28e+112)))
   (+ x (/ (- z y) (/ (- z) a)))
   (- x (* a (/ y (- (+ t 1.0) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+32) || !(z <= 1.28e+112)) {
		tmp = x + ((z - y) / (-z / a));
	} else {
		tmp = x - (a * (y / ((t + 1.0) - 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 <= (-1.5d+32)) .or. (.not. (z <= 1.28d+112))) then
        tmp = x + ((z - y) / (-z / a))
    else
        tmp = x - (a * (y / ((t + 1.0d0) - 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 <= -1.5e+32) || !(z <= 1.28e+112)) {
		tmp = x + ((z - y) / (-z / a));
	} else {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+32) or not (z <= 1.28e+112):
		tmp = x + ((z - y) / (-z / a))
	else:
		tmp = x - (a * (y / ((t + 1.0) - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+32) || !(z <= 1.28e+112))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(-z) / a)));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(Float64(t + 1.0) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.5e+32) || ~((z <= 1.28e+112)))
		tmp = x + ((z - y) / (-z / a));
	else
		tmp = x - (a * (y / ((t + 1.0) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+32], N[Not[LessEqual[z, 1.28e+112]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e32 or 1.28e112 < z

   1. Initial program 93.3%

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

   2. Taylor expanded in z around inf 84.1%

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

      1. mul-1-neg 84.1%

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

      2. distribute-neg-frac 84.1%

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

   4. Simplified 84.1%

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

   if -1.5e32 < z < 1.28e112

   1. Initial program 98.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 89.6%

      \[\leadsto x - \color{blue}{\frac{y}{\left(1 + t\right) - z}} \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+32} \lor \neg \left(z \leq 1.28 \cdot 10^{+112}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \end{array} \]

Alternative 8: 88.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+133} \lor \neg \left(y \leq 3.7 \cdot 10^{-47}\right):\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.4e+133) (not (<= y 3.7e-47)))
   (- x (* a (/ y (- (+ t 1.0) z))))
   (+ x (* a (/ z (+ (- t z) 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.4e+133) || !(y <= 3.7e-47)) {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	} else {
		tmp = x + (a * (z / ((t - 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 <= (-3.4d+133)) .or. (.not. (y <= 3.7d-47))) then
        tmp = x - (a * (y / ((t + 1.0d0) - z)))
    else
        tmp = x + (a * (z / ((t - 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 <= -3.4e+133) || !(y <= 3.7e-47)) {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	} else {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.4e+133) or not (y <= 3.7e-47):
		tmp = x - (a * (y / ((t + 1.0) - z)))
	else:
		tmp = x + (a * (z / ((t - z) + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.4e+133) || !(y <= 3.7e-47))
		tmp = Float64(x - Float64(a * Float64(y / Float64(Float64(t + 1.0) - z))));
	else
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(t - z) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.4e+133) || ~((y <= 3.7e-47)))
		tmp = x - (a * (y / ((t + 1.0) - z)));
	else
		tmp = x + (a * (z / ((t - z) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.4e+133], N[Not[LessEqual[y, 3.7e-47]], $MachinePrecision]], N[(x - N[(a * N[(y / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(z / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999987e133 or 3.7e-47 < y

   1. Initial program 97.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 88.1%

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

   if -3.39999999999999987e133 < y < 3.7e-47

   1. Initial program 95.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 95.4%

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

      1. associate-*r/ 95.4%

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

      2. neg-mul-1 95.4%

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

      3. associate--l+ 95.4%

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

   6. Simplified 95.4%

      \[\leadsto x - \color{blue}{\frac{-z}{1 + \left(t - z\right)}} \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+133} \lor \neg \left(y \leq 3.7 \cdot 10^{-47}\right):\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \end{array} \]

Alternative 9: 86.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+29} \lor \neg \left(z \leq 2.55 \cdot 10^{-16}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3e+29) (not (<= z 2.55e-16)))
   (+ x (/ (- z y) (/ (- z) a)))
   (- x (/ a (/ (+ t 1.0) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e+29) || !(z <= 2.55e-16)) {
		tmp = x + ((z - y) / (-z / a));
	} else {
		tmp = x - (a / ((t + 1.0) / 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 <= (-3d+29)) .or. (.not. (z <= 2.55d-16))) then
        tmp = x + ((z - y) / (-z / a))
    else
        tmp = x - (a / ((t + 1.0d0) / 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 <= -3e+29) || !(z <= 2.55e-16)) {
		tmp = x + ((z - y) / (-z / a));
	} else {
		tmp = x - (a / ((t + 1.0) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3e+29) or not (z <= 2.55e-16):
		tmp = x + ((z - y) / (-z / a))
	else:
		tmp = x - (a / ((t + 1.0) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3e+29) || !(z <= 2.55e-16))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(-z) / a)));
	else
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3e+29) || ~((z <= 2.55e-16)))
		tmp = x + ((z - y) / (-z / a));
	else
		tmp = x - (a / ((t + 1.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3e+29], N[Not[LessEqual[z, 2.55e-16]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9999999999999999e29 or 2.55e-16 < z

   1. Initial program 94.5%

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

   2. Taylor expanded in z around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. distribute-neg-frac 82.1%

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

   4. Simplified 82.1%

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

   if -2.9999999999999999e29 < z < 2.55e-16

   1. Initial program 98.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*l/ 92.6%

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

   5. Applied egg-rr 92.6%

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

   6. Taylor expanded in z around 0 83.3%

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

      1. associate-/l* 90.6%

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

   8. Simplified 90.6%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+29} \lor \neg \left(z \leq 2.55 \cdot 10^{-16}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \]

Alternative 10: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-12}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+126}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e-12)
   (- x a)
   (if (<= z 2.55e-16)
     (- x (* y a))
     (if (<= z 3.5e+126) (+ x (* y (/ a z))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e-12) {
		tmp = x - a;
	} else if (z <= 2.55e-16) {
		tmp = x - (y * a);
	} else if (z <= 3.5e+126) {
		tmp = x + (y * (a / z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8d-12)) then
        tmp = x - a
    else if (z <= 2.55d-16) then
        tmp = x - (y * a)
    else if (z <= 3.5d+126) then
        tmp = x + (y * (a / z))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e-12) {
		tmp = x - a;
	} else if (z <= 2.55e-16) {
		tmp = x - (y * a);
	} else if (z <= 3.5e+126) {
		tmp = x + (y * (a / z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e-12:
		tmp = x - a
	elif z <= 2.55e-16:
		tmp = x - (y * a)
	elif z <= 3.5e+126:
		tmp = x + (y * (a / z))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e-12)
		tmp = Float64(x - a);
	elseif (z <= 2.55e-16)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 3.5e+126)
		tmp = Float64(x + Float64(y * Float64(a / z)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e-12)
		tmp = x - a;
	elseif (z <= 2.55e-16)
		tmp = x - (y * a);
	elseif (z <= 3.5e+126)
		tmp = x + (y * (a / z));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e-12], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.55e-16], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+126], N[(x + N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.99999999999999984e-12 or 3.5000000000000003e126 < z

   1. Initial program 92.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 79.2%

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

   if -7.99999999999999984e-12 < z < 2.55e-16

   1. Initial program 99.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 72.2%

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

   5. Taylor expanded in z around 0 68.3%

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

   if 2.55e-16 < z < 3.5000000000000003e126

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 86.6%

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

   5. Taylor expanded in z around inf 71.6%

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

      1. associate-/l* 74.8%

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

   7. Simplified 74.8%

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

      1. associate-/r/ 74.9%

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

   9. Applied egg-rr 74.9%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-12}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+126}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 11: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+32}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+126}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e+32)
   (- x a)
   (if (<= z 2.55e-16)
     (- x (* y (/ a (+ t 1.0))))
     (if (<= z 4.6e+126) (+ x (* y (/ a z))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+32) {
		tmp = x - a;
	} else if (z <= 2.55e-16) {
		tmp = x - (y * (a / (t + 1.0)));
	} else if (z <= 4.6e+126) {
		tmp = x + (y * (a / z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.8d+32)) then
        tmp = x - a
    else if (z <= 2.55d-16) then
        tmp = x - (y * (a / (t + 1.0d0)))
    else if (z <= 4.6d+126) then
        tmp = x + (y * (a / z))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+32) {
		tmp = x - a;
	} else if (z <= 2.55e-16) {
		tmp = x - (y * (a / (t + 1.0)));
	} else if (z <= 4.6e+126) {
		tmp = x + (y * (a / z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e+32:
		tmp = x - a
	elif z <= 2.55e-16:
		tmp = x - (y * (a / (t + 1.0)))
	elif z <= 4.6e+126:
		tmp = x + (y * (a / z))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e+32)
		tmp = Float64(x - a);
	elseif (z <= 2.55e-16)
		tmp = Float64(x - Float64(y * Float64(a / Float64(t + 1.0))));
	elseif (z <= 4.6e+126)
		tmp = Float64(x + Float64(y * Float64(a / z)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e+32)
		tmp = x - a;
	elseif (z <= 2.55e-16)
		tmp = x - (y * (a / (t + 1.0)));
	elseif (z <= 4.6e+126)
		tmp = x + (y * (a / z));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e+32], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.55e-16], N[(x - N[(y * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+126], N[(x + N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.80000000000000004e32 or 4.6000000000000001e126 < z

   1. Initial program 93.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.0%

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

   if -8.80000000000000004e32 < z < 2.55e-16

   1. Initial program 98.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 83.3%

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

      1. associate-/l* 90.6%

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

      2. associate-/r/ 89.6%

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

   6. Simplified 89.6%

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

   if 2.55e-16 < z < 4.6000000000000001e126

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 86.6%

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

   5. Taylor expanded in z around inf 71.6%

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

      1. associate-/l* 74.8%

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

   7. Simplified 74.8%

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

      1. associate-/r/ 74.9%

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

   9. Applied egg-rr 74.9%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+32}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+126}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 12: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+31}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-16}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+130}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e+31)
   (- x a)
   (if (<= z 2.55e-16)
     (- x (/ a (/ (+ t 1.0) y)))
     (if (<= z 4.6e+130) (+ x (* y (/ a z))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+31) {
		tmp = x - a;
	} else if (z <= 2.55e-16) {
		tmp = x - (a / ((t + 1.0) / y));
	} else if (z <= 4.6e+130) {
		tmp = x + (y * (a / z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7d+31)) then
        tmp = x - a
    else if (z <= 2.55d-16) then
        tmp = x - (a / ((t + 1.0d0) / y))
    else if (z <= 4.6d+130) then
        tmp = x + (y * (a / z))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+31) {
		tmp = x - a;
	} else if (z <= 2.55e-16) {
		tmp = x - (a / ((t + 1.0) / y));
	} else if (z <= 4.6e+130) {
		tmp = x + (y * (a / z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e+31:
		tmp = x - a
	elif z <= 2.55e-16:
		tmp = x - (a / ((t + 1.0) / y))
	elif z <= 4.6e+130:
		tmp = x + (y * (a / z))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e+31)
		tmp = Float64(x - a);
	elseif (z <= 2.55e-16)
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	elseif (z <= 4.6e+130)
		tmp = Float64(x + Float64(y * Float64(a / z)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7e+31)
		tmp = x - a;
	elseif (z <= 2.55e-16)
		tmp = x - (a / ((t + 1.0) / y));
	elseif (z <= 4.6e+130)
		tmp = x + (y * (a / z));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e+31], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.55e-16], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+130], N[(x + N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7e31 or 4.60000000000000042e130 < z

   1. Initial program 93.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.0%

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

   if -7e31 < z < 2.55e-16

   1. Initial program 98.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*l/ 92.6%

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

   5. Applied egg-rr 92.6%

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

   6. Taylor expanded in z around 0 83.3%

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

      1. associate-/l* 90.6%

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

   8. Simplified 90.6%

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

   if 2.55e-16 < z < 4.60000000000000042e130

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 86.6%

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

   5. Taylor expanded in z around inf 71.6%

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

      1. associate-/l* 74.8%

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

   7. Simplified 74.8%

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

      1. associate-/r/ 74.9%

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

   9. Applied egg-rr 74.9%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+31}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-16}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+130}:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 13: 66.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-37}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-41}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.65e-37) (- x a) (if (<= z 1.65e-41) (+ x (* z a)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e-37) {
		tmp = x - a;
	} else if (z <= 1.65e-41) {
		tmp = x + (z * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.65d-37)) then
        tmp = x - a
    else if (z <= 1.65d-41) then
        tmp = x + (z * a)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e-37) {
		tmp = x - a;
	} else if (z <= 1.65e-41) {
		tmp = x + (z * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.65e-37:
		tmp = x - a
	elif z <= 1.65e-41:
		tmp = x + (z * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.65e-37)
		tmp = Float64(x - a);
	elseif (z <= 1.65e-41)
		tmp = Float64(x + Float64(z * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.65e-37)
		tmp = x - a;
	elseif (z <= 1.65e-41)
		tmp = x + (z * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.65e-37], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.65e-41], N[(x + N[(z * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.64999999999999991e-37 or 1.65000000000000012e-41 < z

   1. Initial program 94.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 72.9%

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

   if -1.64999999999999991e-37 < z < 1.65000000000000012e-41

   1. Initial program 99.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 64.7%

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

      1. associate-*r/ 64.7%

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

      2. neg-mul-1 64.7%

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

      3. associate--l+ 64.7%

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

   6. Simplified 64.7%

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

   7. Taylor expanded in t around 0 60.5%

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

      1. sub-neg 60.5%

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

      2. mul-1-neg 60.5%

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

      3. remove-double-neg 60.5%

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

      4. associate-/l* 60.5%

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

   9. Simplified 60.5%

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

   10. Taylor expanded in z around 0 60.5%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-37}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-41}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 14: 70.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-13}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-144}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e-13) (- x a) (if (<= z 5.5e-144) (- x (* y a)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e-13) {
		tmp = x - a;
	} else if (z <= 5.5e-144) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.4d-13)) then
        tmp = x - a
    else if (z <= 5.5d-144) then
        tmp = x - (y * a)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e-13) {
		tmp = x - a;
	} else if (z <= 5.5e-144) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e-13:
		tmp = x - a
	elif z <= 5.5e-144:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e-13)
		tmp = Float64(x - a);
	elseif (z <= 5.5e-144)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.4e-13)
		tmp = x - a;
	elseif (z <= 5.5e-144)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e-13], N[(x - a), $MachinePrecision], If[LessEqual[z, 5.5e-144], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.39999999999999993e-13 or 5.49999999999999973e-144 < z

   1. Initial program 94.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 73.1%

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

   if -4.39999999999999993e-13 < z < 5.49999999999999973e-144

   1. Initial program 98.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 73.3%

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

   5. Taylor expanded in z around 0 69.4%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-13}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-144}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 15: 65.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-38}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e-38) (- x a) (if (<= z 3.6e+60) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e-38) {
		tmp = x - a;
	} else if (z <= 3.6e+60) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.25d-38)) then
        tmp = x - a
    else if (z <= 3.6d+60) then
        tmp = x
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e-38) {
		tmp = x - a;
	} else if (z <= 3.6e+60) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e-38:
		tmp = x - a
	elif z <= 3.6e+60:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e-38)
		tmp = Float64(x - a);
	elseif (z <= 3.6e+60)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.25e-38)
		tmp = x - a;
	elseif (z <= 3.6e+60)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e-38], N[(x - a), $MachinePrecision], If[LessEqual[z, 3.6e+60], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25000000000000008e-38 or 3.59999999999999968e60 < z

   1. Initial program 93.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 75.6%

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

   if -1.25000000000000008e-38 < z < 3.59999999999999968e60

   1. Initial program 99.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Step-by-step derivation

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 90.4%

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

   5. Taylor expanded in x around inf 59.1%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-38}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 16: 53.8% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 96.2%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Step-by-step derivation

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around inf 72.9%

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

5. Taylor expanded in x around inf 49.4%

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

6. Final simplification 49.4%

   \[\leadsto x \]

Developer target: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\left(t - z\right) + 1} \cdot a \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (* (/ (- y z) (+ (- t z) 1.0)) a)))

C

double code(double x, double y, double z, double t, double a) {
	return x - (((y - z) / ((t - z) + 1.0)) * a);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x - (((y - z) / ((t - z) + 1.0d0)) * a)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - (((y - z) / ((t - z) + 1.0)) * a);
}

Python

def code(x, y, z, t, a):
	return x - (((y - z) / ((t - z) + 1.0)) * a)

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(Float64(y - z) / Float64(Float64(t - z) + 1.0)) * a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - (((y - z) / ((t - z) + 1.0)) * a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(N[(y - z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023257 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))