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

Percentage Accurate: 97.0% → 99.6%

Time: 10.1s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.8%

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

   1. associate-/r/ 99.2%

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

   2. *-commutative 99.2%

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

3. Simplified 99.2%

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

   1. clear-num 99.2%

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

   2. un-div-inv 99.2%

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

5. Applied egg-rr 99.2%

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

6. Final simplification 99.2%

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

Alternative 2: 71.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{-1 + \frac{1}{z}}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+231}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-152}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (+ -1.0 (/ 1.0 z))))))
   (if (<= t -1.35e+231)
     (+ x (/ a (/ t z)))
     (if (<= t -1.35e-292)
       t_1
       (if (<= t 3.4e-152)
         (- x (* a y))
         (if (<= t 7.2e+74) 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 + (1.0 / z)));
	double tmp;
	if (t <= -1.35e+231) {
		tmp = x + (a / (t / z));
	} else if (t <= -1.35e-292) {
		tmp = t_1;
	} else if (t <= 3.4e-152) {
		tmp = x - (a * y);
	} else if (t <= 7.2e+74) {
		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) + (1.0d0 / z)))
    if (t <= (-1.35d+231)) then
        tmp = x + (a / (t / z))
    else if (t <= (-1.35d-292)) then
        tmp = t_1
    else if (t <= 3.4d-152) then
        tmp = x - (a * y)
    else if (t <= 7.2d+74) 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 + (1.0 / z)));
	double tmp;
	if (t <= -1.35e+231) {
		tmp = x + (a / (t / z));
	} else if (t <= -1.35e-292) {
		tmp = t_1;
	} else if (t <= 3.4e-152) {
		tmp = x - (a * y);
	} else if (t <= 7.2e+74) {
		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 + (1.0 / z)))
	tmp = 0
	if t <= -1.35e+231:
		tmp = x + (a / (t / z))
	elif t <= -1.35e-292:
		tmp = t_1
	elif t <= 3.4e-152:
		tmp = x - (a * y)
	elif t <= 7.2e+74:
		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(-1.0 + Float64(1.0 / z))))
	tmp = 0.0
	if (t <= -1.35e+231)
		tmp = Float64(x + Float64(a / Float64(t / z)));
	elseif (t <= -1.35e-292)
		tmp = t_1;
	elseif (t <= 3.4e-152)
		tmp = Float64(x - Float64(a * y));
	elseif (t <= 7.2e+74)
		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 + (1.0 / z)));
	tmp = 0.0;
	if (t <= -1.35e+231)
		tmp = x + (a / (t / z));
	elseif (t <= -1.35e-292)
		tmp = t_1;
	elseif (t <= 3.4e-152)
		tmp = x - (a * y);
	elseif (t <= 7.2e+74)
		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[(-1.0 + N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+231], N[(x + N[(a / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e-292], t$95$1, If[LessEqual[t, 3.4e-152], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+74], t$95$1, N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.35e231

   1. Initial program 95.1%

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

      1. associate-/r/ 94.7%

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

      2. *-commutative 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around inf 89.6%

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

   5. Taylor expanded in y around 0 64.8%

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

      1. mul-1-neg 64.8%

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

      2. associate-/l* 74.9%

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

   7. Simplified 74.9%

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

   if -1.35e231 < t < -1.35e-292 or 3.39999999999999984e-152 < t < 7.19999999999999975e74

   1. Initial program 95.1%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 87.4%

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

   5. Taylor expanded in y around 0 70.1%

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

      1. sub-neg 70.1%

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

      2. mul-1-neg 70.1%

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

      3. remove-double-neg 70.1%

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

      4. associate-/l* 78.8%

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

      5. div-sub 78.8%

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

      6. *-inverses 78.8%

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

   7. Simplified 78.8%

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

   if -1.35e-292 < t < 3.39999999999999984e-152

   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%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 74.9%

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

      1. associate-/l* 74.9%

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

   6. Simplified 74.9%

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

   7. Taylor expanded in t around 0 74.9%

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

   if 7.19999999999999975e74 < t

   1. Initial program 90.5%

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

      1. associate-/r/ 98.0%

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

      2. *-commutative 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t around inf 89.4%

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

   5. Taylor expanded in y around inf 72.4%

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

      1. associate-/l* 82.1%

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

   7. Simplified 82.1%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+231}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-292}:\\ \;\;\;\;x + \frac{a}{-1 + \frac{1}{z}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-152}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+74}:\\ \;\;\;\;x + \frac{a}{-1 + \frac{1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]

Alternative 3: 86.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+174}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+133}:\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e+174)
   (- x a)
   (if (<= z 4e+133) (- x (* a (/ y (- (+ t 1.0) z)))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+174) {
		tmp = x - a;
	} else if (z <= 4e+133) {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.2d+174)) then
        tmp = x - a
    else if (z <= 4d+133) then
        tmp = x - (a * (y / ((t + 1.0d0) - z)))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+174) {
		tmp = x - a;
	} else if (z <= 4e+133) {
		tmp = x - (a * (y / ((t + 1.0) - z)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e+174:
		tmp = x - a
	elif z <= 4e+133:
		tmp = x - (a * (y / ((t + 1.0) - z)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+174)
		tmp = Float64(x - a);
	elseif (z <= 4e+133)
		tmp = Float64(x - Float64(a * Float64(y / Float64(Float64(t + 1.0) - z))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.2e+174)
		tmp = x - a;
	elseif (z <= 4e+133)
		tmp = x - (a * (y / ((t + 1.0) - z)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e+174], N[(x - a), $MachinePrecision], If[LessEqual[z, 4e+133], N[(x - N[(a * N[(y / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.20000000000000033e174 or 4.0000000000000001e133 < z

   1. Initial program 91.3%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 87.1%

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

   if -4.20000000000000033e174 < z < 4.0000000000000001e133

   1. Initial program 96.0%

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

      1. associate-/r/ 98.9%

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

      2. *-commutative 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around inf 86.2%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+174}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+133}:\\ \;\;\;\;x - a \cdot \frac{y}{\left(t + 1\right) - z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 4: 91.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+51}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+74}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8e+51)
   (- x (* (- y z) (/ a t)))
   (if (<= t 1.5e+74)
     (+ x (* a (/ (- z y) (- 1.0 z))))
     (+ x (* a (/ (- z y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8e+51) {
		tmp = x - ((y - z) * (a / t));
	} else if (t <= 1.5e+74) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else {
		tmp = x + (a * ((z - y) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-8d+51)) then
        tmp = x - ((y - z) * (a / t))
    else if (t <= 1.5d+74) then
        tmp = x + (a * ((z - y) / (1.0d0 - z)))
    else
        tmp = x + (a * ((z - y) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8e+51) {
		tmp = x - ((y - z) * (a / t));
	} else if (t <= 1.5e+74) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else {
		tmp = x + (a * ((z - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8e+51:
		tmp = x - ((y - z) * (a / t))
	elif t <= 1.5e+74:
		tmp = x + (a * ((z - y) / (1.0 - z)))
	else:
		tmp = x + (a * ((z - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8e+51)
		tmp = Float64(x - Float64(Float64(y - z) * Float64(a / t)));
	elseif (t <= 1.5e+74)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(1.0 - z))));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -8e+51)
		tmp = x - ((y - z) * (a / t));
	elseif (t <= 1.5e+74)
		tmp = x + (a * ((z - y) / (1.0 - z)));
	else
		tmp = x + (a * ((z - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8e+51], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+74], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8e51

   1. Initial program 96.7%

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

      1. associate-/r/ 98.3%

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

      2. *-commutative 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around inf 75.0%

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

      1. associate-/l* 82.8%

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

      2. associate-/r/ 84.2%

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

   6. Simplified 84.2%

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

   if -8e51 < t < 1.5e74

   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%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 96.7%

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

   if 1.5e74 < t

   1. Initial program 90.5%

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

      1. associate-/r/ 98.0%

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

      2. *-commutative 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t around inf 89.4%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+51}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+74}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]

Alternative 5: 90.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -13:\\ \;\;\;\;x + a \cdot \frac{z}{t + \left(1 - z\right)}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+72}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -13.0)
   (+ x (* a (/ z (+ t (- 1.0 z)))))
   (if (<= t 4.8e+72)
     (+ x (* a (/ (- z y) (- 1.0 z))))
     (+ x (* a (/ (- z y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -13.0) {
		tmp = x + (a * (z / (t + (1.0 - z))));
	} else if (t <= 4.8e+72) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else {
		tmp = x + (a * ((z - y) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-13.0d0)) then
        tmp = x + (a * (z / (t + (1.0d0 - z))))
    else if (t <= 4.8d+72) then
        tmp = x + (a * ((z - y) / (1.0d0 - z)))
    else
        tmp = x + (a * ((z - y) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -13.0) {
		tmp = x + (a * (z / (t + (1.0 - z))));
	} else if (t <= 4.8e+72) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else {
		tmp = x + (a * ((z - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -13.0:
		tmp = x + (a * (z / (t + (1.0 - z))))
	elif t <= 4.8e+72:
		tmp = x + (a * ((z - y) / (1.0 - z)))
	else:
		tmp = x + (a * ((z - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -13.0)
		tmp = Float64(x + Float64(a * Float64(z / Float64(t + Float64(1.0 - z)))));
	elseif (t <= 4.8e+72)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(1.0 - z))));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -13.0)
		tmp = x + (a * (z / (t + (1.0 - z))));
	elseif (t <= 4.8e+72)
		tmp = x + (a * ((z - y) / (1.0 - z)));
	else
		tmp = x + (a * ((z - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -13.0], N[(x + N[(a * N[(z / N[(t + N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+72], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -13

   1. Initial program 96.2%

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

      1. associate-/r/ 98.5%

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

      2. *-commutative 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in y around 0 87.6%

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

      1. associate-*r/ 87.6%

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

      2. neg-mul-1 87.6%

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

      3. +-commutative 87.6%

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

      4. associate--l+ 87.6%

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

   6. Simplified 87.6%

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

   if -13 < t < 4.8000000000000002e72

   1. Initial program 95.7%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 97.3%

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

   if 4.8000000000000002e72 < t

   1. Initial program 90.5%

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

      1. associate-/r/ 98.0%

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

      2. *-commutative 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t around inf 89.4%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -13:\\ \;\;\;\;x + a \cdot \frac{z}{t + \left(1 - z\right)}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+72}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]

Alternative 6: 90.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1250:\\ \;\;\;\;x + \frac{a}{\frac{t + 1}{z} + -1}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+72}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1250.0)
   (+ x (/ a (+ (/ (+ t 1.0) z) -1.0)))
   (if (<= t 5e+72)
     (+ x (* a (/ (- z y) (- 1.0 z))))
     (+ x (* a (/ (- z y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1250.0) {
		tmp = x + (a / (((t + 1.0) / z) + -1.0));
	} else if (t <= 5e+72) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else {
		tmp = x + (a * ((z - y) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1250.0d0)) then
        tmp = x + (a / (((t + 1.0d0) / z) + (-1.0d0)))
    else if (t <= 5d+72) then
        tmp = x + (a * ((z - y) / (1.0d0 - z)))
    else
        tmp = x + (a * ((z - y) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1250.0) {
		tmp = x + (a / (((t + 1.0) / z) + -1.0));
	} else if (t <= 5e+72) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else {
		tmp = x + (a * ((z - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1250.0:
		tmp = x + (a / (((t + 1.0) / z) + -1.0))
	elif t <= 5e+72:
		tmp = x + (a * ((z - y) / (1.0 - z)))
	else:
		tmp = x + (a * ((z - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1250.0)
		tmp = Float64(x + Float64(a / Float64(Float64(Float64(t + 1.0) / z) + -1.0)));
	elseif (t <= 5e+72)
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(1.0 - z))));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1250.0)
		tmp = x + (a / (((t + 1.0) / z) + -1.0));
	elseif (t <= 5e+72)
		tmp = x + (a * ((z - y) / (1.0 - z)));
	else
		tmp = x + (a * ((z - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1250.0], N[(x + N[(a / N[(N[(N[(t + 1.0), $MachinePrecision] / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+72], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1250

   1. Initial program 96.2%

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

      1. associate-/r/ 98.5%

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

      2. *-commutative 98.5%

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

   3. Simplified 98.5%

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

      1. clear-num 98.5%

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

      2. un-div-inv 98.5%

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

   5. Applied egg-rr 98.5%

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

   6. Taylor expanded in y around 0 73.9%

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

      1. mul-1-neg 73.9%

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

      2. associate-/l* 87.6%

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

      3. distribute-neg-frac 87.6%

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

      4. div-sub 87.6%

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

      5. sub-neg 87.6%

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

      6. *-inverses 87.6%

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

      7. metadata-eval 87.6%

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

   8. Simplified 87.6%

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

   if -1250 < t < 4.99999999999999992e72

   1. Initial program 95.7%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 97.3%

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

   if 4.99999999999999992e72 < t

   1. Initial program 90.5%

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

      1. associate-/r/ 98.0%

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

      2. *-commutative 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in t around inf 89.4%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1250:\\ \;\;\;\;x + \frac{a}{\frac{t + 1}{z} + -1}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+72}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]

Alternative 7: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-257}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.1:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y t)))))
   (if (<= t -3.6e+134)
     t_1
     (if (<= t -5.6e-257) (- x a) (if (<= t 1.1) (- x (* a y)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / t));
	double tmp;
	if (t <= -3.6e+134) {
		tmp = t_1;
	} else if (t <= -5.6e-257) {
		tmp = x - a;
	} else if (t <= 1.1) {
		tmp = x - (a * y);
	} 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 - (a * (y / t))
    if (t <= (-3.6d+134)) then
        tmp = t_1
    else if (t <= (-5.6d-257)) then
        tmp = x - a
    else if (t <= 1.1d0) then
        tmp = x - (a * y)
    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 - (a * (y / t));
	double tmp;
	if (t <= -3.6e+134) {
		tmp = t_1;
	} else if (t <= -5.6e-257) {
		tmp = x - a;
	} else if (t <= 1.1) {
		tmp = x - (a * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (y / t))
	tmp = 0
	if t <= -3.6e+134:
		tmp = t_1
	elif t <= -5.6e-257:
		tmp = x - a
	elif t <= 1.1:
		tmp = x - (a * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / t)))
	tmp = 0.0
	if (t <= -3.6e+134)
		tmp = t_1;
	elseif (t <= -5.6e-257)
		tmp = Float64(x - a);
	elseif (t <= 1.1)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (y / t));
	tmp = 0.0;
	if (t <= -3.6e+134)
		tmp = t_1;
	elseif (t <= -5.6e-257)
		tmp = x - a;
	elseif (t <= 1.1)
		tmp = x - (a * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+134], t$95$1, If[LessEqual[t, -5.6e-257], N[(x - a), $MachinePrecision], If[LessEqual[t, 1.1], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.59999999999999988e134 or 1.1000000000000001 < t

   1. Initial program 92.1%

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

      1. associate-/r/ 98.1%

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

      2. *-commutative 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around inf 85.5%

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

   5. Taylor expanded in y around inf 76.5%

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

   if -3.59999999999999988e134 < t < -5.60000000000000002e-257

   1. Initial program 95.7%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.2%

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

   if -5.60000000000000002e-257 < t < 1.1000000000000001

   1. Initial program 98.4%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 71.9%

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

      1. associate-/l* 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in t around 0 71.9%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+134}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-257}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1.1:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]

Alternative 8: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -6.4 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-253}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ a (/ t y)))))
   (if (<= t -6.4e+133)
     t_1
     (if (<= t -5.4e-253) (- x a) (if (<= t 1.0) (- x (* a y)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a / (t / y));
	double tmp;
	if (t <= -6.4e+133) {
		tmp = t_1;
	} else if (t <= -5.4e-253) {
		tmp = x - a;
	} else if (t <= 1.0) {
		tmp = x - (a * y);
	} 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 - (a / (t / y))
    if (t <= (-6.4d+133)) then
        tmp = t_1
    else if (t <= (-5.4d-253)) then
        tmp = x - a
    else if (t <= 1.0d0) then
        tmp = x - (a * y)
    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 - (a / (t / y));
	double tmp;
	if (t <= -6.4e+133) {
		tmp = t_1;
	} else if (t <= -5.4e-253) {
		tmp = x - a;
	} else if (t <= 1.0) {
		tmp = x - (a * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a / (t / y))
	tmp = 0
	if t <= -6.4e+133:
		tmp = t_1
	elif t <= -5.4e-253:
		tmp = x - a
	elif t <= 1.0:
		tmp = x - (a * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a / Float64(t / y)))
	tmp = 0.0
	if (t <= -6.4e+133)
		tmp = t_1;
	elseif (t <= -5.4e-253)
		tmp = Float64(x - a);
	elseif (t <= 1.0)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a / (t / y));
	tmp = 0.0;
	if (t <= -6.4e+133)
		tmp = t_1;
	elseif (t <= -5.4e-253)
		tmp = x - a;
	elseif (t <= 1.0)
		tmp = x - (a * y);
	else
		tmp = t_1;
	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]}, If[LessEqual[t, -6.4e+133], t$95$1, If[LessEqual[t, -5.4e-253], N[(x - a), $MachinePrecision], If[LessEqual[t, 1.0], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.39999999999999994e133 or 1 < t

   1. Initial program 92.1%

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

      1. associate-/r/ 98.1%

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

      2. *-commutative 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around inf 85.5%

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

   5. Taylor expanded in y around inf 70.3%

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

      1. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

   if -6.39999999999999994e133 < t < -5.39999999999999998e-253

   1. Initial program 95.7%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.2%

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

   if -5.39999999999999998e-253 < t < 1

   1. Initial program 98.4%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 71.9%

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

      1. associate-/l* 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in t around 0 71.9%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+133}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-253}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]

Alternative 9: 68.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+135}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-252}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e+135)
   (+ x (/ a (/ t z)))
   (if (<= t -3.4e-252)
     (- x a)
     (if (<= t 1.0) (- x (* a y)) (- x (/ a (/ t y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+135) {
		tmp = x + (a / (t / z));
	} else if (t <= -3.4e-252) {
		tmp = x - a;
	} else if (t <= 1.0) {
		tmp = x - (a * y);
	} 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) :: tmp
    if (t <= (-2.1d+135)) then
        tmp = x + (a / (t / z))
    else if (t <= (-3.4d-252)) then
        tmp = x - a
    else if (t <= 1.0d0) then
        tmp = x - (a * y)
    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 tmp;
	if (t <= -2.1e+135) {
		tmp = x + (a / (t / z));
	} else if (t <= -3.4e-252) {
		tmp = x - a;
	} else if (t <= 1.0) {
		tmp = x - (a * y);
	} else {
		tmp = x - (a / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.1e+135:
		tmp = x + (a / (t / z))
	elif t <= -3.4e-252:
		tmp = x - a
	elif t <= 1.0:
		tmp = x - (a * y)
	else:
		tmp = x - (a / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e+135)
		tmp = Float64(x + Float64(a / Float64(t / z)));
	elseif (t <= -3.4e-252)
		tmp = Float64(x - a);
	elseif (t <= 1.0)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = Float64(x - Float64(a / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.1e+135)
		tmp = x + (a / (t / z));
	elseif (t <= -3.4e-252)
		tmp = x - a;
	elseif (t <= 1.0)
		tmp = x - (a * y);
	else
		tmp = x - (a / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e+135], N[(x + N[(a / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.4e-252], N[(x - a), $MachinePrecision], If[LessEqual[t, 1.0], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.1000000000000001e135

   1. Initial program 95.5%

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

      1. associate-/r/ 97.7%

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

      2. *-commutative 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in t around inf 87.0%

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

   5. Taylor expanded in y around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. associate-/l* 76.3%

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

   7. Simplified 76.3%

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

   if -2.1000000000000001e135 < t < -3.4e-252

   1. Initial program 95.7%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.2%

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

   if -3.4e-252 < t < 1

   1. Initial program 98.4%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 71.9%

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

      1. associate-/l* 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in t around 0 71.9%

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

   if 1 < t

   1. Initial program 89.7%

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

      1. associate-/r/ 98.4%

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

      2. *-commutative 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in t around inf 84.5%

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

   5. Taylor expanded in y around inf 69.7%

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

      1. associate-/l* 77.2%

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

   7. Simplified 77.2%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+135}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-252}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]

Alternative 10: 83.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+173}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+24}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+173)
   (- x a)
   (if (<= z 8.8e+24) (- 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 <= -1.45e+173) {
		tmp = x - a;
	} else if (z <= 8.8e+24) {
		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 <= (-1.45d+173)) then
        tmp = x - a
    else if (z <= 8.8d+24) 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 <= -1.45e+173) {
		tmp = x - a;
	} else if (z <= 8.8e+24) {
		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 <= -1.45e+173:
		tmp = x - a
	elif z <= 8.8e+24:
		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 <= -1.45e+173)
		tmp = Float64(x - a);
	elseif (z <= 8.8e+24)
		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 <= -1.45e+173)
		tmp = x - a;
	elseif (z <= 8.8e+24)
		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, -1.45e+173], N[(x - a), $MachinePrecision], If[LessEqual[z, 8.8e+24], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45000000000000003e173 or 8.80000000000000007e24 < z

   1. Initial program 91.3%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.8%

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

   if -1.45000000000000003e173 < z < 8.80000000000000007e24

   1. Initial program 96.6%

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

      1. associate-/r/ 98.8%

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

      2. *-commutative 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 86.2%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+173}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+24}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 11: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+173}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+25}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.5e+173)
   (- x a)
   (if (<= z 1.35e+25) (- x (/ a (/ (+ t 1.0) y))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+173) {
		tmp = x - a;
	} else if (z <= 1.35e+25) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.5d+173)) then
        tmp = x - a
    else if (z <= 1.35d+25) then
        tmp = x - (a / ((t + 1.0d0) / y))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.5e+173) {
		tmp = x - a;
	} else if (z <= 1.35e+25) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.5e+173:
		tmp = x - a
	elif z <= 1.35e+25:
		tmp = x - (a / ((t + 1.0) / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.5e+173)
		tmp = Float64(x - a);
	elseif (z <= 1.35e+25)
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.5e+173)
		tmp = x - a;
	elseif (z <= 1.35e+25)
		tmp = x - (a / ((t + 1.0) / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.5e+173], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.35e+25], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4999999999999999e173 or 1.35e25 < z

   1. Initial program 91.3%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.8%

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

   if -1.4999999999999999e173 < z < 1.35e25

   1. Initial program 96.6%

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

      1. associate-/r/ 98.8%

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

      2. *-commutative 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 82.9%

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

      1. associate-/l* 86.3%

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

   6. Simplified 86.3%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+173}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+25}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 12: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.8%

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

   1. associate-/r/ 99.2%

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

   2. *-commutative 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 13: 72.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-7}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+22}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e-7) (- x a) (if (<= z 3.05e+22) (- x (* a y)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e-7) {
		tmp = x - a;
	} else if (z <= 3.05e+22) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.5d-7)) then
        tmp = x - a
    else if (z <= 3.05d+22) then
        tmp = x - (a * y)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e-7) {
		tmp = x - a;
	} else if (z <= 3.05e+22) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e-7:
		tmp = x - a
	elif z <= 3.05e+22:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e-7)
		tmp = Float64(x - a);
	elseif (z <= 3.05e+22)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e-7)
		tmp = x - a;
	elseif (z <= 3.05e+22)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e-7], N[(x - a), $MachinePrecision], If[LessEqual[z, 3.05e+22], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000014e-7 or 3.0499999999999999e22 < z

   1. Initial program 92.5%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 74.0%

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

   if -8.50000000000000014e-7 < z < 3.0499999999999999e22

   1. Initial program 97.1%

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

      1. associate-/r/ 98.5%

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

      2. *-commutative 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in z around 0 90.7%

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

      1. associate-/l* 92.9%

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

   6. Simplified 92.9%

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

   7. Taylor expanded in t around 0 74.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-7}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+22}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 14: 66.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+15}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.4e+15) (- x a) (if (<= z 3.1e+22) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.4e+15) {
		tmp = x - a;
	} else if (z <= 3.1e+22) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.4d+15)) then
        tmp = x - a
    else if (z <= 3.1d+22) then
        tmp = x
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.4e+15) {
		tmp = x - a;
	} else if (z <= 3.1e+22) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.4e+15:
		tmp = x - a
	elif z <= 3.1e+22:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.4e+15)
		tmp = Float64(x - a);
	elseif (z <= 3.1e+22)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.4e+15)
		tmp = x - a;
	elseif (z <= 3.1e+22)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.4e+15], N[(x - a), $MachinePrecision], If[LessEqual[z, 3.1e+22], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4e15 or 3.1000000000000002e22 < z

   1. Initial program 92.4%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 74.5%

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

   if -8.4e15 < z < 3.1000000000000002e22

   1. Initial program 97.1%

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

      1. associate-/r/ 98.5%

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

      2. *-commutative 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in t around 0 76.1%

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

   5. Taylor expanded in x around inf 63.9%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+15}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 15: 53.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+235}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= z -2.6e+235) (- a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+235) {
		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 (z <= (-2.6d+235)) 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 (z <= -2.6e+235) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+235:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+235)
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+235)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+235], (-a), x]

Derivation

1. Split input into 2 regimes

2. if z < -2.5999999999999998e235

   1. Initial program 87.8%

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

      1. associate-/r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 95.4%

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

   5. Taylor expanded in x around 0 23.0%

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

      1. mul-1-neg 23.0%

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

      2. associate-*r/ 83.2%

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

      3. distribute-lft-neg-in 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in z around inf 77.9%

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

      1. mul-1-neg 77.9%

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

   10. Simplified 77.9%

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

   if -2.5999999999999998e235 < z

   1. Initial program 95.3%

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

      1. associate-/r/ 99.1%

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

      2. *-commutative 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in t around 0 77.6%

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

   5. Taylor expanded in x around inf 59.3%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+235}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 53.8% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.8%

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

   1. associate-/r/ 99.2%

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

   2. *-commutative 99.2%

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

3. Simplified 99.2%

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

4. Taylor expanded in t around 0 78.7%

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

5. Taylor expanded in x around inf 56.5%

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

6. Final simplification 56.5%

   \[\leadsto x \]

Developer target: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023297 
(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))))