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

Percentage Accurate: 97.3% → 99.8%

Time: 11.3s

Alternatives: 12

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: 97.3% 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: 99.8% 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 97.3%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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. Final simplification 99.9%

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

Alternative 2: 71.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -5 \cdot 10^{+113}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+39}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -0.0034:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-264}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -5e+113)
     (- x a)
     (if (<= z -4.3e+39)
       (+ x (* a (/ z t)))
       (if (<= z -0.0034)
         (- x a)
         (if (<= z -1.9e-144)
           t_1
           (if (<= z -2.8e-264)
             (- x (* a (/ y t)))
             (if (<= z 8.2e-8) t_1 (- 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 <= -5e+113) {
		tmp = x - a;
	} else if (z <= -4.3e+39) {
		tmp = x + (a * (z / t));
	} else if (z <= -0.0034) {
		tmp = x - a;
	} else if (z <= -1.9e-144) {
		tmp = t_1;
	} else if (z <= -2.8e-264) {
		tmp = x - (a * (y / t));
	} else if (z <= 8.2e-8) {
		tmp = t_1;
	} 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 <= (-5d+113)) then
        tmp = x - a
    else if (z <= (-4.3d+39)) then
        tmp = x + (a * (z / t))
    else if (z <= (-0.0034d0)) then
        tmp = x - a
    else if (z <= (-1.9d-144)) then
        tmp = t_1
    else if (z <= (-2.8d-264)) then
        tmp = x - (a * (y / t))
    else if (z <= 8.2d-8) then
        tmp = t_1
    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 <= -5e+113) {
		tmp = x - a;
	} else if (z <= -4.3e+39) {
		tmp = x + (a * (z / t));
	} else if (z <= -0.0034) {
		tmp = x - a;
	} else if (z <= -1.9e-144) {
		tmp = t_1;
	} else if (z <= -2.8e-264) {
		tmp = x - (a * (y / t));
	} else if (z <= 8.2e-8) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	tmp = 0
	if z <= -5e+113:
		tmp = x - a
	elif z <= -4.3e+39:
		tmp = x + (a * (z / t))
	elif z <= -0.0034:
		tmp = x - a
	elif z <= -1.9e-144:
		tmp = t_1
	elif z <= -2.8e-264:
		tmp = x - (a * (y / t))
	elif z <= 8.2e-8:
		tmp = t_1
	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 <= -5e+113)
		tmp = Float64(x - a);
	elseif (z <= -4.3e+39)
		tmp = Float64(x + Float64(a * Float64(z / t)));
	elseif (z <= -0.0034)
		tmp = Float64(x - a);
	elseif (z <= -1.9e-144)
		tmp = t_1;
	elseif (z <= -2.8e-264)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= 8.2e-8)
		tmp = t_1;
	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 <= -5e+113)
		tmp = x - a;
	elseif (z <= -4.3e+39)
		tmp = x + (a * (z / t));
	elseif (z <= -0.0034)
		tmp = x - a;
	elseif (z <= -1.9e-144)
		tmp = t_1;
	elseif (z <= -2.8e-264)
		tmp = x - (a * (y / t));
	elseif (z <= 8.2e-8)
		tmp = t_1;
	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, -5e+113], N[(x - a), $MachinePrecision], If[LessEqual[z, -4.3e+39], N[(x + N[(a * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.0034], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.9e-144], t$95$1, If[LessEqual[z, -2.8e-264], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-8], t$95$1, N[(x - a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5e113 or -4.3e39 < z < -0.00339999999999999981 or 8.20000000000000063e-8 < z

   1. Initial program 95.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 86.4%

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

   if -5e113 < z < -4.3e39

   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 inf 72.4%

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

   5. Taylor expanded in y around 0 79.5%

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

      1. neg-mul-1 79.5%

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

      2. distribute-neg-frac 79.5%

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

   7. Simplified 79.5%

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

   if -0.00339999999999999981 < z < -1.89999999999999996e-144 or -2.80000000000000012e-264 < z < 8.20000000000000063e-8

   1. Initial program 98.7%

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

      1. associate-/r/ 98.7%

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

      2. div-inv 98.7%

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

      3. associate-/r* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in t around 0 83.1%

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

   7. Taylor expanded in z around 0 81.3%

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

   if -1.89999999999999996e-144 < z < -2.80000000000000012e-264

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 87.8%

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

   5. Taylor expanded in y around inf 87.8%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+113}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+39}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -0.0034:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-144}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-264}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 3: 72.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+172}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-148}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (/ (- 1.0 z) z)))))
   (if (<= t -2.05e+172)
     (- x (* a (/ y t)))
     (if (<= t -4.2e-226)
       t_1
       (if (<= t 1e-148)
         (- x (* y a))
         (if (<= t 1.95e+96) t_1 (- x (/ a (/ t y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / ((1.0 - z) / z));
	double tmp;
	if (t <= -2.05e+172) {
		tmp = x - (a * (y / t));
	} else if (t <= -4.2e-226) {
		tmp = t_1;
	} else if (t <= 1e-148) {
		tmp = x - (y * a);
	} else if (t <= 1.95e+96) {
		tmp = t_1;
	} else {
		tmp = x - (a / (t / 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) :: t_1
    real(8) :: tmp
    t_1 = x + (a / ((1.0d0 - z) / z))
    if (t <= (-2.05d+172)) then
        tmp = x - (a * (y / t))
    else if (t <= (-4.2d-226)) then
        tmp = t_1
    else if (t <= 1d-148) then
        tmp = x - (y * a)
    else if (t <= 1.95d+96) then
        tmp = t_1
    else
        tmp = x - (a / (t / y))
    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 + (a / ((1.0 - z) / z));
	double tmp;
	if (t <= -2.05e+172) {
		tmp = x - (a * (y / t));
	} else if (t <= -4.2e-226) {
		tmp = t_1;
	} else if (t <= 1e-148) {
		tmp = x - (y * a);
	} else if (t <= 1.95e+96) {
		tmp = t_1;
	} else {
		tmp = x - (a / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a / ((1.0 - z) / z))
	tmp = 0
	if t <= -2.05e+172:
		tmp = x - (a * (y / t))
	elif t <= -4.2e-226:
		tmp = t_1
	elif t <= 1e-148:
		tmp = x - (y * a)
	elif t <= 1.95e+96:
		tmp = t_1
	else:
		tmp = x - (a / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a / Float64(Float64(1.0 - z) / z)))
	tmp = 0.0
	if (t <= -2.05e+172)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (t <= -4.2e-226)
		tmp = t_1;
	elseif (t <= 1e-148)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 1.95e+96)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(a / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a / ((1.0 - z) / z));
	tmp = 0.0;
	if (t <= -2.05e+172)
		tmp = x - (a * (y / t));
	elseif (t <= -4.2e-226)
		tmp = t_1;
	elseif (t <= 1e-148)
		tmp = x - (y * a);
	elseif (t <= 1.95e+96)
		tmp = t_1;
	else
		tmp = x - (a / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a / N[(N[(1.0 - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.05e+172], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.2e-226], t$95$1, If[LessEqual[t, 1e-148], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+96], t$95$1, N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.05e172

   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 inf 99.9%

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

   5. Taylor expanded in y around inf 83.3%

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

   if -2.05e172 < t < -4.2000000000000003e-226 or 9.99999999999999936e-149 < t < 1.95e96

   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. Step-by-step derivation

      1. associate-/r/ 98.5%

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

      2. div-inv 98.5%

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

      3. associate-/r* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in t around 0 94.4%

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

   7. Taylor expanded in y around 0 81.1%

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

      1. sub-neg 81.1%

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

      2. mul-1-neg 81.1%

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

      3. remove-double-neg 81.1%

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

      4. associate-/l* 87.2%

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

   9. Simplified 87.2%

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

   if -4.2000000000000003e-226 < t < 9.99999999999999936e-149

   1. Initial program 94.0%

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

      1. associate-/r/ 94.0%

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

      2. div-inv 93.9%

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

      3. associate-/r* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around 0 99.8%

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

   7. Taylor expanded in z around 0 72.2%

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

   if 1.95e96 < t

   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 t around inf 90.9%

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

   5. Taylor expanded in y around inf 83.7%

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

      1. associate-/l* 85.8%

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

   7. Simplified 85.8%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+172}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-226}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{elif}\;t \leq 10^{-148}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+96}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]

Alternative 4: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+113}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+39}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -0.0029:\\ \;\;\;\;x + z \cdot \frac{a}{1 - z}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+63}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e+113)
   (- x a)
   (if (<= z -2.8e+39)
     (+ x (* a (/ z t)))
     (if (<= z -0.0029)
       (+ x (* z (/ a (- 1.0 z))))
       (if (<= z 7.6e+63) (- x (* a (/ y (+ t 1.0)))) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e+113) {
		tmp = x - a;
	} else if (z <= -2.8e+39) {
		tmp = x + (a * (z / t));
	} else if (z <= -0.0029) {
		tmp = x + (z * (a / (1.0 - z)));
	} else if (z <= 7.6e+63) {
		tmp = x - (a * (y / (t + 1.0)));
	} 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 <= (-5d+113)) then
        tmp = x - a
    else if (z <= (-2.8d+39)) then
        tmp = x + (a * (z / t))
    else if (z <= (-0.0029d0)) then
        tmp = x + (z * (a / (1.0d0 - z)))
    else if (z <= 7.6d+63) then
        tmp = x - (a * (y / (t + 1.0d0)))
    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 <= -5e+113) {
		tmp = x - a;
	} else if (z <= -2.8e+39) {
		tmp = x + (a * (z / t));
	} else if (z <= -0.0029) {
		tmp = x + (z * (a / (1.0 - z)));
	} else if (z <= 7.6e+63) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5e+113:
		tmp = x - a
	elif z <= -2.8e+39:
		tmp = x + (a * (z / t))
	elif z <= -0.0029:
		tmp = x + (z * (a / (1.0 - z)))
	elif z <= 7.6e+63:
		tmp = x - (a * (y / (t + 1.0)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e+113)
		tmp = Float64(x - a);
	elseif (z <= -2.8e+39)
		tmp = Float64(x + Float64(a * Float64(z / t)));
	elseif (z <= -0.0029)
		tmp = Float64(x + Float64(z * Float64(a / Float64(1.0 - z))));
	elseif (z <= 7.6e+63)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5e+113)
		tmp = x - a;
	elseif (z <= -2.8e+39)
		tmp = x + (a * (z / t));
	elseif (z <= -0.0029)
		tmp = x + (z * (a / (1.0 - z)));
	elseif (z <= 7.6e+63)
		tmp = x - (a * (y / (t + 1.0)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e+113], N[(x - a), $MachinePrecision], If[LessEqual[z, -2.8e+39], N[(x + N[(a * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.0029], N[(x + N[(z * N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e+63], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5e113 or 7.6000000000000002e63 < z

   1. Initial program 93.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 91.2%

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

   if -5e113 < z < -2.80000000000000001e39

   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 inf 72.4%

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

   5. Taylor expanded in y around 0 79.5%

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

      1. neg-mul-1 79.5%

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

      2. distribute-neg-frac 79.5%

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

   7. Simplified 79.5%

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

   if -2.80000000000000001e39 < z < -0.0029

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 99.7%

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

   3. Taylor expanded in y around 0 92.0%

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

      1. cancel-sign-sub-inv 92.0%

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

      2. metadata-eval 92.0%

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

      3. *-lft-identity 92.0%

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

      4. +-commutative 92.0%

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

      5. associate-/l* 91.9%

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

      6. associate-/r/ 92.0%

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

   5. Simplified 92.0%

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

   if -0.0029 < z < 7.6000000000000002e63

   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 z around 0 91.9%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+113}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+39}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -0.0029:\\ \;\;\;\;x + z \cdot \frac{a}{1 - z}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+63}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 5: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+39}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -0.0046:\\ \;\;\;\;x + z \cdot \frac{a}{1 - z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- (* y (/ a z)) a))))
   (if (<= z -5.3e+91)
     t_1
     (if (<= z -1.05e+39)
       (+ x (* a (/ z t)))
       (if (<= z -0.0046)
         (+ x (* z (/ a (- 1.0 z))))
         (if (<= z 8.2e-8) (- x (* a (/ y (+ t 1.0)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (a / z)) - a);
	double tmp;
	if (z <= -5.3e+91) {
		tmp = t_1;
	} else if (z <= -1.05e+39) {
		tmp = x + (a * (z / t));
	} else if (z <= -0.0046) {
		tmp = x + (z * (a / (1.0 - z)));
	} else if (z <= 8.2e-8) {
		tmp = x - (a * (y / (t + 1.0)));
	} 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 * (a / z)) - a)
    if (z <= (-5.3d+91)) then
        tmp = t_1
    else if (z <= (-1.05d+39)) then
        tmp = x + (a * (z / t))
    else if (z <= (-0.0046d0)) then
        tmp = x + (z * (a / (1.0d0 - z)))
    else if (z <= 8.2d-8) then
        tmp = x - (a * (y / (t + 1.0d0)))
    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 * (a / z)) - a);
	double tmp;
	if (z <= -5.3e+91) {
		tmp = t_1;
	} else if (z <= -1.05e+39) {
		tmp = x + (a * (z / t));
	} else if (z <= -0.0046) {
		tmp = x + (z * (a / (1.0 - z)));
	} else if (z <= 8.2e-8) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * (a / z)) - a)
	tmp = 0
	if z <= -5.3e+91:
		tmp = t_1
	elif z <= -1.05e+39:
		tmp = x + (a * (z / t))
	elif z <= -0.0046:
		tmp = x + (z * (a / (1.0 - z)))
	elif z <= 8.2e-8:
		tmp = x - (a * (y / (t + 1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * Float64(a / z)) - a))
	tmp = 0.0
	if (z <= -5.3e+91)
		tmp = t_1;
	elseif (z <= -1.05e+39)
		tmp = Float64(x + Float64(a * Float64(z / t)));
	elseif (z <= -0.0046)
		tmp = Float64(x + Float64(z * Float64(a / Float64(1.0 - z))));
	elseif (z <= 8.2e-8)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * (a / z)) - a);
	tmp = 0.0;
	if (z <= -5.3e+91)
		tmp = t_1;
	elseif (z <= -1.05e+39)
		tmp = x + (a * (z / t));
	elseif (z <= -0.0046)
		tmp = x + (z * (a / (1.0 - z)));
	elseif (z <= 8.2e-8)
		tmp = x - (a * (y / (t + 1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.3e+91], t$95$1, If[LessEqual[z, -1.05e+39], N[(x + N[(a * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.0046], N[(x + N[(z * N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-8], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.29999999999999997e91 or 8.20000000000000063e-8 < z

   1. Initial program 94.7%

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

   2. Taylor expanded in z around inf 89.1%

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

      1. associate-*r/ 89.1%

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

      2. neg-mul-1 89.1%

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

   4. Simplified 89.1%

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

   5. Taylor expanded in y around 0 90.2%

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

      1. mul-1-neg 90.2%

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

      2. unsub-neg 90.2%

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

      3. *-commutative 90.2%

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

      4. associate-*r/ 94.3%

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

   7. Simplified 94.3%

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

   if -5.29999999999999997e91 < z < -1.0499999999999999e39

   1. Initial program 99.9%

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

      1. associate-/r/ 99.8%

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

   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 81.5%

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

   5. Taylor expanded in y around 0 85.3%

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

      1. neg-mul-1 85.3%

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

      2. distribute-neg-frac 85.3%

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

   7. Simplified 85.3%

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

   if -1.0499999999999999e39 < z < -0.0045999999999999999

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 99.7%

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

   3. Taylor expanded in y around 0 92.0%

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

      1. cancel-sign-sub-inv 92.0%

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

      2. metadata-eval 92.0%

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

      3. *-lft-identity 92.0%

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

      4. +-commutative 92.0%

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

      5. associate-/l* 91.9%

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

      6. associate-/r/ 92.0%

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

   5. Simplified 92.0%

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

   if -0.0045999999999999999 < z < 8.20000000000000063e-8

   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 z around 0 94.3%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+91}:\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+39}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -0.0046:\\ \;\;\;\;x + z \cdot \frac{a}{1 - z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \end{array} \]

Alternative 6: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+39}:\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq -0.0054:\\ \;\;\;\;x + z \cdot \frac{a}{1 - z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- (* y (/ a z)) a))))
   (if (<= z -5.3e+91)
     t_1
     (if (<= z -3.4e+39)
       (- x (/ (- y z) (/ t a)))
       (if (<= z -0.0054)
         (+ x (* z (/ a (- 1.0 z))))
         (if (<= z 8.2e-8) (- x (* a (/ y (+ t 1.0)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (a / z)) - a);
	double tmp;
	if (z <= -5.3e+91) {
		tmp = t_1;
	} else if (z <= -3.4e+39) {
		tmp = x - ((y - z) / (t / a));
	} else if (z <= -0.0054) {
		tmp = x + (z * (a / (1.0 - z)));
	} else if (z <= 8.2e-8) {
		tmp = x - (a * (y / (t + 1.0)));
	} 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 * (a / z)) - a)
    if (z <= (-5.3d+91)) then
        tmp = t_1
    else if (z <= (-3.4d+39)) then
        tmp = x - ((y - z) / (t / a))
    else if (z <= (-0.0054d0)) then
        tmp = x + (z * (a / (1.0d0 - z)))
    else if (z <= 8.2d-8) then
        tmp = x - (a * (y / (t + 1.0d0)))
    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 * (a / z)) - a);
	double tmp;
	if (z <= -5.3e+91) {
		tmp = t_1;
	} else if (z <= -3.4e+39) {
		tmp = x - ((y - z) / (t / a));
	} else if (z <= -0.0054) {
		tmp = x + (z * (a / (1.0 - z)));
	} else if (z <= 8.2e-8) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * (a / z)) - a)
	tmp = 0
	if z <= -5.3e+91:
		tmp = t_1
	elif z <= -3.4e+39:
		tmp = x - ((y - z) / (t / a))
	elif z <= -0.0054:
		tmp = x + (z * (a / (1.0 - z)))
	elif z <= 8.2e-8:
		tmp = x - (a * (y / (t + 1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * Float64(a / z)) - a))
	tmp = 0.0
	if (z <= -5.3e+91)
		tmp = t_1;
	elseif (z <= -3.4e+39)
		tmp = Float64(x - Float64(Float64(y - z) / Float64(t / a)));
	elseif (z <= -0.0054)
		tmp = Float64(x + Float64(z * Float64(a / Float64(1.0 - z))));
	elseif (z <= 8.2e-8)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * (a / z)) - a);
	tmp = 0.0;
	if (z <= -5.3e+91)
		tmp = t_1;
	elseif (z <= -3.4e+39)
		tmp = x - ((y - z) / (t / a));
	elseif (z <= -0.0054)
		tmp = x + (z * (a / (1.0 - z)));
	elseif (z <= 8.2e-8)
		tmp = x - (a * (y / (t + 1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.3e+91], t$95$1, If[LessEqual[z, -3.4e+39], N[(x - N[(N[(y - z), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.0054], N[(x + N[(z * N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-8], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.29999999999999997e91 or 8.20000000000000063e-8 < z

   1. Initial program 94.7%

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

   2. Taylor expanded in z around inf 89.1%

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

      1. associate-*r/ 89.1%

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

      2. neg-mul-1 89.1%

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

   4. Simplified 89.1%

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

   5. Taylor expanded in y around 0 90.2%

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

      1. mul-1-neg 90.2%

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

      2. unsub-neg 90.2%

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

      3. *-commutative 90.2%

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

      4. associate-*r/ 94.3%

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

   7. Simplified 94.3%

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

   if -5.29999999999999997e91 < z < -3.3999999999999999e39

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 87.5%

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

   if -3.3999999999999999e39 < z < -0.0054000000000000003

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 99.7%

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

   3. Taylor expanded in y around 0 92.0%

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

      1. cancel-sign-sub-inv 92.0%

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

      2. metadata-eval 92.0%

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

      3. *-lft-identity 92.0%

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

      4. +-commutative 92.0%

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

      5. associate-/l* 91.9%

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

      6. associate-/r/ 92.0%

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

   5. Simplified 92.0%

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

   if -0.0054000000000000003 < z < 8.20000000000000063e-8

   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 z around 0 94.3%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+91}:\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+39}:\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq -0.0054:\\ \;\;\;\;x + z \cdot \frac{a}{1 - z}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \end{array} \]

Alternative 7: 91.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+115} \lor \neg \left(t \leq 4.2 \cdot 10^{+96}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9e+115) (not (<= t 4.2e+96)))
   (+ x (* a (/ (- z y) t)))
   (+ x (* a (/ (- z y) (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9e+115) || !(t <= 4.2e+96)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x + (a * ((z - y) / (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 ((t <= (-9d+115)) .or. (.not. (t <= 4.2d+96))) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = x + (a * ((z - y) / (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 ((t <= -9e+115) || !(t <= 4.2e+96)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9e+115) or not (t <= 4.2e+96):
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x + (a * ((z - y) / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9e+115) || !(t <= 4.2e+96))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9e+115) || ~((t <= 4.2e+96)))
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x + (a * ((z - y) / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9e+115], N[Not[LessEqual[t, 4.2e+96]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.99999999999999927e115 or 4.2000000000000002e96 < t

   1. Initial program 97.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around inf 94.5%

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

   if -8.99999999999999927e115 < t < 4.2000000000000002e96

   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 t around 0 97.5%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+115} \lor \neg \left(t \leq 4.2 \cdot 10^{+96}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \]

Alternative 8: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -0.00058:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-263}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -0.00058)
     (- x a)
     (if (<= z -1.4e-143)
       t_1
       (if (<= z -5.8e-263)
         (- x (* a (/ y t)))
         (if (<= z 8e-8) t_1 (- 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 <= -0.00058) {
		tmp = x - a;
	} else if (z <= -1.4e-143) {
		tmp = t_1;
	} else if (z <= -5.8e-263) {
		tmp = x - (a * (y / t));
	} else if (z <= 8e-8) {
		tmp = t_1;
	} 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 <= (-0.00058d0)) then
        tmp = x - a
    else if (z <= (-1.4d-143)) then
        tmp = t_1
    else if (z <= (-5.8d-263)) then
        tmp = x - (a * (y / t))
    else if (z <= 8d-8) then
        tmp = t_1
    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 <= -0.00058) {
		tmp = x - a;
	} else if (z <= -1.4e-143) {
		tmp = t_1;
	} else if (z <= -5.8e-263) {
		tmp = x - (a * (y / t));
	} else if (z <= 8e-8) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	tmp = 0
	if z <= -0.00058:
		tmp = x - a
	elif z <= -1.4e-143:
		tmp = t_1
	elif z <= -5.8e-263:
		tmp = x - (a * (y / t))
	elif z <= 8e-8:
		tmp = t_1
	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 <= -0.00058)
		tmp = Float64(x - a);
	elseif (z <= -1.4e-143)
		tmp = t_1;
	elseif (z <= -5.8e-263)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= 8e-8)
		tmp = t_1;
	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 <= -0.00058)
		tmp = x - a;
	elseif (z <= -1.4e-143)
		tmp = t_1;
	elseif (z <= -5.8e-263)
		tmp = x - (a * (y / t));
	elseif (z <= 8e-8)
		tmp = t_1;
	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, -0.00058], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.4e-143], t$95$1, If[LessEqual[z, -5.8e-263], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-8], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8e-4 or 8.0000000000000002e-8 < 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 z around inf 81.5%

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

   if -5.8e-4 < z < -1.3999999999999999e-143 or -5.80000000000000007e-263 < z < 8.0000000000000002e-8

   1. Initial program 98.7%

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

      1. associate-/r/ 98.7%

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

      2. div-inv 98.7%

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

      3. associate-/r* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in t around 0 83.1%

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

   7. Taylor expanded in z around 0 81.3%

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

   if -1.3999999999999999e-143 < z < -5.80000000000000007e-263

   1. Initial program 100.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 87.8%

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

   5. Taylor expanded in y around inf 87.8%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00058:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-143}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-263}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-8}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 9: 88.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{a}{\frac{t - \left(z + -1\right)}{z}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e-7)
   (+ x (/ a (/ (- t (+ z -1.0)) z)))
   (if (<= z 8.2e-8) (- x (* a (/ y (+ t 1.0)))) (+ x (- (* y (/ a z)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e-7) {
		tmp = x + (a / ((t - (z + -1.0)) / z));
	} else if (z <= 8.2e-8) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = x + ((y * (a / z)) - 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 <= (-1.1d-7)) then
        tmp = x + (a / ((t - (z + (-1.0d0))) / z))
    else if (z <= 8.2d-8) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else
        tmp = x + ((y * (a / z)) - 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 <= -1.1e-7) {
		tmp = x + (a / ((t - (z + -1.0)) / z));
	} else if (z <= 8.2e-8) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = x + ((y * (a / z)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e-7:
		tmp = x + (a / ((t - (z + -1.0)) / z))
	elif z <= 8.2e-8:
		tmp = x - (a * (y / (t + 1.0)))
	else:
		tmp = x + ((y * (a / z)) - a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e-7)
		tmp = Float64(x + Float64(a / Float64(Float64(t - Float64(z + -1.0)) / z)));
	elseif (z <= 8.2e-8)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(a / z)) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e-7)
		tmp = x + (a / ((t - (z + -1.0)) / z));
	elseif (z <= 8.2e-8)
		tmp = x - (a * (y / (t + 1.0)));
	else
		tmp = x + ((y * (a / z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e-7], N[(x + N[(a / N[(N[(t - N[(z + -1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-8], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1000000000000001e-7

   1. Initial program 97.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 y around 0 80.7%

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

      1. sub-neg 80.7%

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

      2. mul-1-neg 80.7%

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

      3. *-commutative 80.7%

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

      4. associate--l+ 80.7%

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

      5. +-commutative 80.7%

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

      6. associate-*r/ 87.2%

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

      7. remove-double-neg 87.2%

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

      8. associate-*r/ 80.7%

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

      9. *-commutative 80.7%

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

      10. +-commutative 80.7%

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

      11. associate--l+ 80.7%

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

      12. associate-/l* 89.8%

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

      13. associate--l+ 89.8%

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

      14. +-commutative 89.8%

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

      15. associate-+l- 89.8%

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

      16. sub-neg 89.8%

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

      17. metadata-eval 89.8%

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

      18. +-commutative 89.8%

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

   6. Simplified 89.8%

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

   if -1.1000000000000001e-7 < z < 8.20000000000000063e-8

   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 z around 0 94.3%

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

   if 8.20000000000000063e-8 < z

   1. Initial program 94.0%

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

   2. Taylor expanded in z around inf 86.2%

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

      1. associate-*r/ 86.2%

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

      2. neg-mul-1 86.2%

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

   4. Simplified 86.2%

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

   5. Taylor expanded in y around 0 87.7%

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

      1. mul-1-neg 87.7%

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

      2. unsub-neg 87.7%

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

      3. *-commutative 87.7%

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

      4. associate-*r/ 92.1%

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

   7. Simplified 92.1%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{a}{\frac{t - \left(z + -1\right)}{z}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \end{array} \]

Alternative 10: 73.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00132 \lor \neg \left(z \leq 8.2 \cdot 10^{-8}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -0.00132) (not (<= z 8.2e-8))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.00132) || !(z <= 8.2e-8)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-0.00132d0)) .or. (.not. (z <= 8.2d-8))) then
        tmp = x - a
    else
        tmp = x - (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.00132) || !(z <= 8.2e-8)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -0.00132) or not (z <= 8.2e-8):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -0.00132) || !(z <= 8.2e-8))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -0.00132) || ~((z <= 8.2e-8)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -0.00132], N[Not[LessEqual[z, 8.2e-8]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.00132 or 8.20000000000000063e-8 < 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 z around inf 81.5%

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

   if -0.00132 < z < 8.20000000000000063e-8

   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. Step-by-step derivation

      1. associate-/r/ 99.0%

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

      2. div-inv 99.0%

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

      3. associate-/r* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in t around 0 80.8%

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

   7. Taylor expanded in z around 0 79.5%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00132 \lor \neg \left(z \leq 8.2 \cdot 10^{-8}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]

Alternative 11: 66.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-6} \lor \neg \left(z \leq 2.3 \cdot 10^{+22}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.35e-6) (not (<= z 2.3e+22))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.35e-6) || !(z <= 2.3e+22)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.35d-6)) .or. (.not. (z <= 2.3d+22))) then
        tmp = x - a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.35e-6) || !(z <= 2.3e+22)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.35e-6) or not (z <= 2.3e+22):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.35e-6) || !(z <= 2.3e+22))
		tmp = Float64(x - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.35e-6) || ~((z <= 2.3e+22)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.35e-6], N[Not[LessEqual[z, 2.3e+22]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.34999999999999995e-6 or 2.3000000000000002e22 < z

   1. Initial program 95.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 82.7%

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

   if -2.34999999999999995e-6 < z < 2.3000000000000002e22

   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 x around inf 67.4%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-6} \lor \neg \left(z \leq 2.3 \cdot 10^{+22}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 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 97.3%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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 x around inf 62.3%

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

5. Final simplification 62.3%

   \[\leadsto x \]

Developer target: 99.8% 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 2023310 
(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))))