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

Percentage Accurate: 96.9% → 99.8%

Time: 12.4s

Alternatives: 13

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: 96.9% 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 98.9%

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

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

Alternative 2: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y - z}{\frac{-z}{a}}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.7:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;z \leq -0.00125:\\ \;\;\;\;a \cdot \frac{z - y}{1 - z}\\ \mathbf{elif}\;z \leq 800000000000:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- y z) (/ (- z) a)))))
   (if (<= z -1.65e+73)
     t_1
     (if (<= z -2.7)
       (+ x (* a (/ (- z y) t)))
       (if (<= z -0.00125)
         (* a (/ (- z y) (- 1.0 z)))
         (if (<= z 800000000000.0) (- x (* y (/ a (+ t 1.0)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) / (-z / a));
	double tmp;
	if (z <= -1.65e+73) {
		tmp = t_1;
	} else if (z <= -2.7) {
		tmp = x + (a * ((z - y) / t));
	} else if (z <= -0.00125) {
		tmp = a * ((z - y) / (1.0 - z));
	} else if (z <= 800000000000.0) {
		tmp = x - (y * (a / (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 - z) / (-z / a))
    if (z <= (-1.65d+73)) then
        tmp = t_1
    else if (z <= (-2.7d0)) then
        tmp = x + (a * ((z - y) / t))
    else if (z <= (-0.00125d0)) then
        tmp = a * ((z - y) / (1.0d0 - z))
    else if (z <= 800000000000.0d0) then
        tmp = x - (y * (a / (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 - z) / (-z / a));
	double tmp;
	if (z <= -1.65e+73) {
		tmp = t_1;
	} else if (z <= -2.7) {
		tmp = x + (a * ((z - y) / t));
	} else if (z <= -0.00125) {
		tmp = a * ((z - y) / (1.0 - z));
	} else if (z <= 800000000000.0) {
		tmp = x - (y * (a / (t + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y - z) / (-z / a))
	tmp = 0
	if z <= -1.65e+73:
		tmp = t_1
	elif z <= -2.7:
		tmp = x + (a * ((z - y) / t))
	elif z <= -0.00125:
		tmp = a * ((z - y) / (1.0 - z))
	elif z <= 800000000000.0:
		tmp = x - (y * (a / (t + 1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) / Float64(Float64(-z) / a)))
	tmp = 0.0
	if (z <= -1.65e+73)
		tmp = t_1;
	elseif (z <= -2.7)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	elseif (z <= -0.00125)
		tmp = Float64(a * Float64(Float64(z - y) / Float64(1.0 - z)));
	elseif (z <= 800000000000.0)
		tmp = Float64(x - Float64(y * Float64(a / 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 - z) / (-z / a));
	tmp = 0.0;
	if (z <= -1.65e+73)
		tmp = t_1;
	elseif (z <= -2.7)
		tmp = x + (a * ((z - y) / t));
	elseif (z <= -0.00125)
		tmp = a * ((z - y) / (1.0 - z));
	elseif (z <= 800000000000.0)
		tmp = x - (y * (a / (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 - z), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+73], t$95$1, If[LessEqual[z, -2.7], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.00125], N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 800000000000.0], N[(x - N[(y * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.65000000000000015e73 or 8e11 < z

   1. Initial program 97.7%

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

   2. Taylor expanded in z around inf 88.9%

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

      1. associate-*r/ 88.9%

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

      2. neg-mul-1 88.9%

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

   4. Simplified 88.9%

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

   if -1.65000000000000015e73 < z < -2.7000000000000002

   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 75.5%

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

   if -2.7000000000000002 < z < -0.00125000000000000003

   1. Initial program 99.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 100.0%

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

   5. Taylor expanded in x around 0 99.5%

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

      1. associate-*r/ 100.0%

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

      2. associate-*r* 100.0%

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

      3. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -0.00125000000000000003 < z < 8e11

   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 z around 0 90.5%

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

      1. associate-/l* 93.7%

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

      2. associate-/r/ 93.7%

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

   6. Simplified 93.7%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{y - z}{\frac{-z}{a}}\\ \mathbf{elif}\;z \leq -2.7:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;z \leq -0.00125:\\ \;\;\;\;a \cdot \frac{z - y}{1 - z}\\ \mathbf{elif}\;z \leq 800000000000:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{-z}{a}}\\ \end{array} \]

Alternative 3: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{a}{\frac{t}{y}}\\ t_2 := x - y \cdot a\\ \mathbf{if}\;z \leq -4 \cdot 10^{+21}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 10^{-213}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ a (/ t y)))) (t_2 (- x (* y a))))
   (if (<= z -4e+21)
     (- x a)
     (if (<= z 1e-213)
       t_2
       (if (<= z 1.66e-155)
         t_1
         (if (<= z 1.2e-78) t_2 (if (<= z 5000000000.0) t_1 (- x a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a / (t / y));
	double t_2 = x - (y * a);
	double tmp;
	if (z <= -4e+21) {
		tmp = x - a;
	} else if (z <= 1e-213) {
		tmp = t_2;
	} else if (z <= 1.66e-155) {
		tmp = t_1;
	} else if (z <= 1.2e-78) {
		tmp = t_2;
	} else if (z <= 5000000000.0) {
		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) :: t_2
    real(8) :: tmp
    t_1 = x - (a / (t / y))
    t_2 = x - (y * a)
    if (z <= (-4d+21)) then
        tmp = x - a
    else if (z <= 1d-213) then
        tmp = t_2
    else if (z <= 1.66d-155) then
        tmp = t_1
    else if (z <= 1.2d-78) then
        tmp = t_2
    else if (z <= 5000000000.0d0) 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 - (a / (t / y));
	double t_2 = x - (y * a);
	double tmp;
	if (z <= -4e+21) {
		tmp = x - a;
	} else if (z <= 1e-213) {
		tmp = t_2;
	} else if (z <= 1.66e-155) {
		tmp = t_1;
	} else if (z <= 1.2e-78) {
		tmp = t_2;
	} else if (z <= 5000000000.0) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a / (t / y))
	t_2 = x - (y * a)
	tmp = 0
	if z <= -4e+21:
		tmp = x - a
	elif z <= 1e-213:
		tmp = t_2
	elif z <= 1.66e-155:
		tmp = t_1
	elif z <= 1.2e-78:
		tmp = t_2
	elif z <= 5000000000.0:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a / Float64(t / y)))
	t_2 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (z <= -4e+21)
		tmp = Float64(x - a);
	elseif (z <= 1e-213)
		tmp = t_2;
	elseif (z <= 1.66e-155)
		tmp = t_1;
	elseif (z <= 1.2e-78)
		tmp = t_2;
	elseif (z <= 5000000000.0)
		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 - (a / (t / y));
	t_2 = x - (y * a);
	tmp = 0.0;
	if (z <= -4e+21)
		tmp = x - a;
	elseif (z <= 1e-213)
		tmp = t_2;
	elseif (z <= 1.66e-155)
		tmp = t_1;
	elseif (z <= 1.2e-78)
		tmp = t_2;
	elseif (z <= 5000000000.0)
		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[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+21], N[(x - a), $MachinePrecision], If[LessEqual[z, 1e-213], t$95$2, If[LessEqual[z, 1.66e-155], t$95$1, If[LessEqual[z, 1.2e-78], t$95$2, If[LessEqual[z, 5000000000.0], t$95$1, N[(x - a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4e21 or 5e9 < z

   1. Initial program 98.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 82.1%

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

   if -4e21 < z < 9.9999999999999995e-214 or 1.65999999999999999e-155 < z < 1.2e-78

   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 82.7%

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

   5. Taylor expanded in z around 0 76.8%

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

   if 9.9999999999999995e-214 < z < 1.65999999999999999e-155 or 1.2e-78 < z < 5e9

   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 85.6%

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

   5. Taylor expanded in y around inf 75.2%

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

      1. associate-/l* 83.2%

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

   7. Simplified 83.2%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+21}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 10^{-213}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-155}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-78}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 5000000000:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 4: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+75}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;z \leq -1.86 \cdot 10^{-6}:\\ \;\;\;\;\frac{y - z}{\frac{z + -1}{a}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+23}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+75)
   (- x a)
   (if (<= z -3.0)
     (+ x (* a (/ (- z y) t)))
     (if (<= z -1.86e-6)
       (/ (- y z) (/ (+ z -1.0) a))
       (if (<= z 8e+23) (- x (* y (/ a (+ t 1.0)))) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+75) {
		tmp = x - a;
	} else if (z <= -3.0) {
		tmp = x + (a * ((z - y) / t));
	} else if (z <= -1.86e-6) {
		tmp = (y - z) / ((z + -1.0) / a);
	} else if (z <= 8e+23) {
		tmp = x - (y * (a / (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 <= (-1.9d+75)) then
        tmp = x - a
    else if (z <= (-3.0d0)) then
        tmp = x + (a * ((z - y) / t))
    else if (z <= (-1.86d-6)) then
        tmp = (y - z) / ((z + (-1.0d0)) / a)
    else if (z <= 8d+23) then
        tmp = x - (y * (a / (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 <= -1.9e+75) {
		tmp = x - a;
	} else if (z <= -3.0) {
		tmp = x + (a * ((z - y) / t));
	} else if (z <= -1.86e-6) {
		tmp = (y - z) / ((z + -1.0) / a);
	} else if (z <= 8e+23) {
		tmp = x - (y * (a / (t + 1.0)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+75:
		tmp = x - a
	elif z <= -3.0:
		tmp = x + (a * ((z - y) / t))
	elif z <= -1.86e-6:
		tmp = (y - z) / ((z + -1.0) / a)
	elif z <= 8e+23:
		tmp = x - (y * (a / (t + 1.0)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+75)
		tmp = Float64(x - a);
	elseif (z <= -3.0)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	elseif (z <= -1.86e-6)
		tmp = Float64(Float64(y - z) / Float64(Float64(z + -1.0) / a));
	elseif (z <= 8e+23)
		tmp = Float64(x - Float64(y * Float64(a / 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 <= -1.9e+75)
		tmp = x - a;
	elseif (z <= -3.0)
		tmp = x + (a * ((z - y) / t));
	elseif (z <= -1.86e-6)
		tmp = (y - z) / ((z + -1.0) / a);
	elseif (z <= 8e+23)
		tmp = x - (y * (a / (t + 1.0)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+75], N[(x - a), $MachinePrecision], If[LessEqual[z, -3.0], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.86e-6], N[(N[(y - z), $MachinePrecision] / N[(N[(z + -1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+23], N[(x - N[(y * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9000000000000001e75 or 7.9999999999999993e23 < z

   1. Initial program 97.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 85.3%

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

   if -1.9000000000000001e75 < z < -3

   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 75.5%

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

   if -3 < z < -1.86e-6

   1. Initial program 99.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 100.0%

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

   5. Taylor expanded in x around 0 99.5%

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

      1. associate-*r/ 100.0%

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

      2. associate-*r* 100.0%

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

      3. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

      1. associate-*r/ 99.5%

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

      2. frac-2neg 99.5%

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

      3. add-sqr-sqrt 99.5%

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

      4. sqrt-unprod 6.9%

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

      5. sqr-neg 6.9%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 0.3%

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

      8. distribute-lft-neg-out 0.3%

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

      9. add-sqr-sqrt 0.3%

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

      10. sqrt-unprod 0.1%

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

      11. sqr-neg 0.1%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 99.5%

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

   9. Applied egg-rr 99.5%

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

       1. *-commutative 99.5%

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

       2. associate-/l* 99.5%

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

       3. neg-sub0 99.5%

          \[\leadsto \frac{y - z}{\frac{\color{blue}{0 - \left(1 - z\right)}}{a}} \]

       4. associate--r- 99.5%

          \[\leadsto \frac{y - z}{\frac{\color{blue}{\left(0 - 1\right) + z}}{a}} \]

       5. metadata-eval 99.5%

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

   11. Simplified 99.5%

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

   if -1.86e-6 < z < 7.9999999999999993e23

   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 z around 0 90.5%

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

      1. associate-/l* 93.7%

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

      2. associate-/r/ 93.7%

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

   6. Simplified 93.7%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+75}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;z \leq -1.86 \cdot 10^{-6}:\\ \;\;\;\;\frac{y - z}{\frac{z + -1}{a}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+23}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 5: 83.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{+74}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -200:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;z \leq -0.00125:\\ \;\;\;\;a \cdot \frac{z - y}{1 - z}\\ \mathbf{elif}\;z \leq 29000000000000:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.3e+74)
   (- x a)
   (if (<= z -200.0)
     (+ x (* a (/ (- z y) t)))
     (if (<= z -0.00125)
       (* a (/ (- z y) (- 1.0 z)))
       (if (<= z 29000000000000.0) (- x (* y (/ a (+ t 1.0)))) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.3e+74) {
		tmp = x - a;
	} else if (z <= -200.0) {
		tmp = x + (a * ((z - y) / t));
	} else if (z <= -0.00125) {
		tmp = a * ((z - y) / (1.0 - z));
	} else if (z <= 29000000000000.0) {
		tmp = x - (y * (a / (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 <= (-6.3d+74)) then
        tmp = x - a
    else if (z <= (-200.0d0)) then
        tmp = x + (a * ((z - y) / t))
    else if (z <= (-0.00125d0)) then
        tmp = a * ((z - y) / (1.0d0 - z))
    else if (z <= 29000000000000.0d0) then
        tmp = x - (y * (a / (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 <= -6.3e+74) {
		tmp = x - a;
	} else if (z <= -200.0) {
		tmp = x + (a * ((z - y) / t));
	} else if (z <= -0.00125) {
		tmp = a * ((z - y) / (1.0 - z));
	} else if (z <= 29000000000000.0) {
		tmp = x - (y * (a / (t + 1.0)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.3e+74:
		tmp = x - a
	elif z <= -200.0:
		tmp = x + (a * ((z - y) / t))
	elif z <= -0.00125:
		tmp = a * ((z - y) / (1.0 - z))
	elif z <= 29000000000000.0:
		tmp = x - (y * (a / (t + 1.0)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.3e+74)
		tmp = Float64(x - a);
	elseif (z <= -200.0)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	elseif (z <= -0.00125)
		tmp = Float64(a * Float64(Float64(z - y) / Float64(1.0 - z)));
	elseif (z <= 29000000000000.0)
		tmp = Float64(x - Float64(y * Float64(a / 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 <= -6.3e+74)
		tmp = x - a;
	elseif (z <= -200.0)
		tmp = x + (a * ((z - y) / t));
	elseif (z <= -0.00125)
		tmp = a * ((z - y) / (1.0 - z));
	elseif (z <= 29000000000000.0)
		tmp = x - (y * (a / (t + 1.0)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.3e+74], N[(x - a), $MachinePrecision], If[LessEqual[z, -200.0], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.00125], N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 29000000000000.0], N[(x - N[(y * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.30000000000000016e74 or 2.9e13 < z

   1. Initial program 97.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 85.3%

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

   if -6.30000000000000016e74 < z < -200

   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 75.5%

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

   if -200 < z < -0.00125000000000000003

   1. Initial program 99.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 100.0%

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

   5. Taylor expanded in x around 0 99.5%

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

      1. associate-*r/ 100.0%

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

      2. associate-*r* 100.0%

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

      3. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -0.00125000000000000003 < z < 2.9e13

   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 z around 0 90.5%

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

      1. associate-/l* 93.7%

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

      2. associate-/r/ 93.7%

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

   6. Simplified 93.7%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{+74}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -200:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;z \leq -0.00125:\\ \;\;\;\;a \cdot \frac{z - y}{1 - z}\\ \mathbf{elif}\;z \leq 29000000000000:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 6: 90.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z - y}{t}\\ \mathbf{if}\;t \leq -2 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+18}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ (- z y) t)))))
   (if (<= t -2e+60)
     t_1
     (if (<= t 4e+18)
       (- x (* a (/ (- y z) (- 1.0 z))))
       (if (<= t 1.5e+64) t_1 (+ x (* a (/ z (+ (- t z) 1.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * ((z - y) / t));
	double tmp;
	if (t <= -2e+60) {
		tmp = t_1;
	} else if (t <= 4e+18) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else if (t <= 1.5e+64) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (a * ((z - y) / t))
    if (t <= (-2d+60)) then
        tmp = t_1
    else if (t <= 4d+18) then
        tmp = x - (a * ((y - z) / (1.0d0 - z)))
    else if (t <= 1.5d+64) then
        tmp = t_1
    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 t_1 = x + (a * ((z - y) / t));
	double tmp;
	if (t <= -2e+60) {
		tmp = t_1;
	} else if (t <= 4e+18) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else if (t <= 1.5e+64) {
		tmp = t_1;
	} else {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * ((z - y) / t))
	tmp = 0
	if t <= -2e+60:
		tmp = t_1
	elif t <= 4e+18:
		tmp = x - (a * ((y - z) / (1.0 - z)))
	elif t <= 1.5e+64:
		tmp = t_1
	else:
		tmp = x + (a * (z / ((t - z) + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(Float64(z - y) / t)))
	tmp = 0.0
	if (t <= -2e+60)
		tmp = t_1;
	elseif (t <= 4e+18)
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(1.0 - z))));
	elseif (t <= 1.5e+64)
		tmp = t_1;
	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)
	t_1 = x + (a * ((z - y) / t));
	tmp = 0.0;
	if (t <= -2e+60)
		tmp = t_1;
	elseif (t <= 4e+18)
		tmp = x - (a * ((y - z) / (1.0 - z)));
	elseif (t <= 1.5e+64)
		tmp = t_1;
	else
		tmp = x + (a * (z / ((t - z) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+60], t$95$1, If[LessEqual[t, 4e+18], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+64], t$95$1, N[(x + N[(a * N[(z / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9999999999999999e60 or 4e18 < t < 1.5000000000000001e64

   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 91.4%

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

   if -1.9999999999999999e60 < t < 4e18

   1. Initial program 98.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 99.1%

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

   if 1.5000000000000001e64 < t

   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 y around 0 93.5%

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

      1. associate--l+ 93.5%

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

      2. +-commutative 93.5%

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

      3. associate-*r/ 93.5%

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

      4. neg-mul-1 93.5%

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

      5. +-commutative 93.5%

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

   6. Simplified 93.5%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+60}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+18}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+64}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \end{array} \]

Alternative 7: 90.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z - y}{t}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+19}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{z + \left(-1 - t\right)}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ (- z y) t)))))
   (if (<= t -6.2e+59)
     t_1
     (if (<= t 2.7e+19)
       (- x (* a (/ (- y z) (- 1.0 z))))
       (if (<= t 1.95e+64) t_1 (- x (/ a (/ (+ z (- -1.0 t)) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * ((z - y) / t));
	double tmp;
	if (t <= -6.2e+59) {
		tmp = t_1;
	} else if (t <= 2.7e+19) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else if (t <= 1.95e+64) {
		tmp = t_1;
	} else {
		tmp = x - (a / ((z + (-1.0 - t)) / 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 + (a * ((z - y) / t))
    if (t <= (-6.2d+59)) then
        tmp = t_1
    else if (t <= 2.7d+19) then
        tmp = x - (a * ((y - z) / (1.0d0 - z)))
    else if (t <= 1.95d+64) then
        tmp = t_1
    else
        tmp = x - (a / ((z + ((-1.0d0) - t)) / 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 + (a * ((z - y) / t));
	double tmp;
	if (t <= -6.2e+59) {
		tmp = t_1;
	} else if (t <= 2.7e+19) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else if (t <= 1.95e+64) {
		tmp = t_1;
	} else {
		tmp = x - (a / ((z + (-1.0 - t)) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * ((z - y) / t))
	tmp = 0
	if t <= -6.2e+59:
		tmp = t_1
	elif t <= 2.7e+19:
		tmp = x - (a * ((y - z) / (1.0 - z)))
	elif t <= 1.95e+64:
		tmp = t_1
	else:
		tmp = x - (a / ((z + (-1.0 - t)) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(Float64(z - y) / t)))
	tmp = 0.0
	if (t <= -6.2e+59)
		tmp = t_1;
	elseif (t <= 2.7e+19)
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(1.0 - z))));
	elseif (t <= 1.95e+64)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(a / Float64(Float64(z + Float64(-1.0 - t)) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a * ((z - y) / t));
	tmp = 0.0;
	if (t <= -6.2e+59)
		tmp = t_1;
	elseif (t <= 2.7e+19)
		tmp = x - (a * ((y - z) / (1.0 - z)));
	elseif (t <= 1.95e+64)
		tmp = t_1;
	else
		tmp = x - (a / ((z + (-1.0 - t)) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+59], t$95$1, If[LessEqual[t, 2.7e+19], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+64], t$95$1, N[(x - N[(a / N[(N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.20000000000000029e59 or 2.7e19 < t < 1.9499999999999999e64

   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 91.4%

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

   if -6.20000000000000029e59 < t < 2.7e19

   1. Initial program 98.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 99.1%

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

   if 1.9499999999999999e64 < t

   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. Step-by-step derivation

      1. associate-*l/ 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-/l* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around 0 93.5%

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

      1. mul-1-neg 93.5%

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

   8. Simplified 93.5%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+59}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+19}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+64}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{z + \left(-1 - t\right)}{z}}\\ \end{array} \]

Alternative 8: 91.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+59} \lor \neg \left(t \leq 3.5 \cdot 10^{+19}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.2e+59) (not (<= t 3.5e+19)))
   (+ x (* a (/ (- z y) t)))
   (- x (* a (/ (- y z) (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.2e+59) || !(t <= 3.5e+19)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - (a * ((y - z) / (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 <= (-6.2d+59)) .or. (.not. (t <= 3.5d+19))) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = x - (a * ((y - z) / (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 <= -6.2e+59) || !(t <= 3.5e+19)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.2e+59) or not (t <= 3.5e+19):
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x - (a * ((y - z) / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.2e+59) || !(t <= 3.5e+19))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.2e+59) || ~((t <= 3.5e+19)))
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x - (a * ((y - z) / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.2e+59], N[Not[LessEqual[t, 3.5e+19]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.20000000000000029e59 or 3.5e19 < t

   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 86.8%

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

   if -6.20000000000000029e59 < t < 3.5e19

   1. Initial program 98.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 99.1%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+59} \lor \neg \left(t \leq 3.5 \cdot 10^{+19}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \end{array} \]

Alternative 9: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+62} \lor \neg \left(z \leq 320000000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e+62) (not (<= z 320000000000.0)))
   (- x a)
   (- x (* y (/ a (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+62) || !(z <= 320000000000.0)) {
		tmp = x - a;
	} else {
		tmp = x - (y * (a / (t + 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 ((z <= (-1.1d+62)) .or. (.not. (z <= 320000000000.0d0))) then
        tmp = x - a
    else
        tmp = x - (y * (a / (t + 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 ((z <= -1.1e+62) || !(z <= 320000000000.0)) {
		tmp = x - a;
	} else {
		tmp = x - (y * (a / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e+62) or not (z <= 320000000000.0):
		tmp = x - a
	else:
		tmp = x - (y * (a / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e+62) || !(z <= 320000000000.0))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * Float64(a / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.1e+62) || ~((z <= 320000000000.0)))
		tmp = x - a;
	else
		tmp = x - (y * (a / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.1e+62], N[Not[LessEqual[z, 320000000000.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.10000000000000007e62 or 3.2e11 < z

   1. Initial program 97.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 84.1%

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

   if -1.10000000000000007e62 < z < 3.2e11

   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 z around 0 85.1%

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

      1. associate-/l* 89.1%

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

      2. associate-/r/ 89.2%

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

   6. Simplified 89.2%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+62} \lor \neg \left(z \leq 320000000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \end{array} \]

Alternative 10: 72.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+21} \lor \neg \left(z \leq 1.8 \cdot 10^{-30}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3e+21) (not (<= z 1.8e-30))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e+21) || !(z <= 1.8e-30)) {
		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 <= (-3d+21)) .or. (.not. (z <= 1.8d-30))) 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 <= -3e+21) || !(z <= 1.8e-30)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3e+21) or not (z <= 1.8e-30):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3e+21) || !(z <= 1.8e-30))
		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 <= -3e+21) || ~((z <= 1.8e-30)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3e+21], N[Not[LessEqual[z, 1.8e-30]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e21 or 1.8000000000000002e-30 < z

   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 inf 79.5%

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

   if -3e21 < z < 1.8000000000000002e-30

   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 76.0%

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

   5. Taylor expanded in z around 0 71.2%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+21} \lor \neg \left(z \leq 1.8 \cdot 10^{-30}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]

Alternative 11: 66.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-7} \lor \neg \left(z \leq 3.6 \cdot 10^{+15}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e-7) (not (<= z 3.6e+15))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e-7) || !(z <= 3.6e+15)) {
		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 <= (-2.8d-7)) .or. (.not. (z <= 3.6d+15))) 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 <= -2.8e-7) || !(z <= 3.6e+15)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.8e-7) or not (z <= 3.6e+15):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e-7) || !(z <= 3.6e+15))
		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 <= -2.8e-7) || ~((z <= 3.6e+15)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e-7], N[Not[LessEqual[z, 3.6e+15]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.80000000000000019e-7 or 3.6e15 < z

   1. Initial program 98.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 79.0%

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

   if -2.80000000000000019e-7 < z < 3.6e15

   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 74.6%

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

   5. Taylor expanded in x around inf 58.5%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-7} \lor \neg \left(z \leq 3.6 \cdot 10^{+15}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 52.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+46}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -2.8e+46) (- a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e+46) {
		tmp = -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 (a <= (-2.8d+46)) then
        tmp = -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 (a <= -2.8e+46) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.8e+46:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.8e+46)
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.8e+46)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.8e+46], (-a), x]

Derivation

1. Split input into 2 regimes

2. if a < -2.80000000000000018e46

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 70.5%

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

   5. Taylor expanded in x around 0 31.4%

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

      1. associate-*r/ 58.3%

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

      2. associate-*r* 58.3%

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

      3. mul-1-neg 58.3%

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

   7. Simplified 58.3%

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

   8. Taylor expanded in z around inf 36.0%

      \[\leadsto \color{blue}{-1 \cdot a} \]
   9. Step-by-step derivation

      1. mul-1-neg 36.0%

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

   10. Simplified 36.0%

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

   if -2.80000000000000018e46 < a

   1. Initial program 98.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 83.8%

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

   5. Taylor expanded in x around inf 60.9%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+46}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 53.9% 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 98.9%

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

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

5. Taylor expanded in x around inf 50.2%

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

6. Final simplification 50.2%

   \[\leadsto x \]

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 2023301 
(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))))