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

Percentage Accurate: 97.2% → 99.6%

Time: 12.0s

Alternatives: 14

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: 97.2% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

   1. sub-neg 95.0%

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

   2. +-commutative 95.0%

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

   3. associate-/r/ 99.9%

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

   4. *-commutative 99.9%

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

   5. distribute-rgt-neg-in 99.9%

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

   6. fma-def 99.9%

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

   7. div-sub 99.9%

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

   8. sub-neg 99.9%

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

   9. +-commutative 99.9%

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

   10. distribute-neg-in 99.9%

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

   11. remove-double-neg 99.9%

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

   12. sub-neg 99.9%

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

   13. div-sub 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 71.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+110}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -0.0085:\\ \;\;\;\;x + \frac{a \cdot y}{z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-141}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ a (/ t y)))))
   (if (<= z -7e+110)
     (- x a)
     (if (<= z -0.0085)
       (+ x (/ (* a y) z))
       (if (<= z -4.5e-198)
         t_1
         (if (<= z 3.1e-141) (- x (* a y)) (if (<= z 9e+43) 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 tmp;
	if (z <= -7e+110) {
		tmp = x - a;
	} else if (z <= -0.0085) {
		tmp = x + ((a * y) / z);
	} else if (z <= -4.5e-198) {
		tmp = t_1;
	} else if (z <= 3.1e-141) {
		tmp = x - (a * y);
	} else if (z <= 9e+43) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (a / (t / y))
    if (z <= (-7d+110)) then
        tmp = x - a
    else if (z <= (-0.0085d0)) then
        tmp = x + ((a * y) / z)
    else if (z <= (-4.5d-198)) then
        tmp = t_1
    else if (z <= 3.1d-141) then
        tmp = x - (a * y)
    else if (z <= 9d+43) 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 tmp;
	if (z <= -7e+110) {
		tmp = x - a;
	} else if (z <= -0.0085) {
		tmp = x + ((a * y) / z);
	} else if (z <= -4.5e-198) {
		tmp = t_1;
	} else if (z <= 3.1e-141) {
		tmp = x - (a * y);
	} else if (z <= 9e+43) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a / (t / y))
	tmp = 0
	if z <= -7e+110:
		tmp = x - a
	elif z <= -0.0085:
		tmp = x + ((a * y) / z)
	elif z <= -4.5e-198:
		tmp = t_1
	elif z <= 3.1e-141:
		tmp = x - (a * y)
	elif z <= 9e+43:
		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)))
	tmp = 0.0
	if (z <= -7e+110)
		tmp = Float64(x - a);
	elseif (z <= -0.0085)
		tmp = Float64(x + Float64(Float64(a * y) / z));
	elseif (z <= -4.5e-198)
		tmp = t_1;
	elseif (z <= 3.1e-141)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 9e+43)
		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));
	tmp = 0.0;
	if (z <= -7e+110)
		tmp = x - a;
	elseif (z <= -0.0085)
		tmp = x + ((a * y) / z);
	elseif (z <= -4.5e-198)
		tmp = t_1;
	elseif (z <= 3.1e-141)
		tmp = x - (a * y);
	elseif (z <= 9e+43)
		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]}, If[LessEqual[z, -7e+110], N[(x - a), $MachinePrecision], If[LessEqual[z, -0.0085], N[(x + N[(N[(a * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.5e-198], t$95$1, If[LessEqual[z, 3.1e-141], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+43], t$95$1, N[(x - a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.9999999999999998e110 or 9e43 < z

   1. Initial program 90.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 87.5%

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

   if -6.9999999999999998e110 < z < -0.0085000000000000006

   1. Initial program 92.0%

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

   2. Taylor expanded in z around inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. distribute-neg-frac 69.7%

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

   4. Simplified 69.7%

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

   5. Taylor expanded in y around inf 64.8%

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

      1. associate-*r/ 64.8%

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

      2. *-commutative 64.8%

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

      3. mul-1-neg 64.8%

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

      4. distribute-rgt-neg-in 64.8%

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

   7. Simplified 64.8%

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

   if -0.0085000000000000006 < z < -4.4999999999999998e-198 or 3.10000000000000027e-141 < z < 9e43

   1. Initial program 99.6%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 57.1%

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

      1. associate-/l* 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in y around inf 73.1%

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

   if -4.4999999999999998e-198 < z < 3.10000000000000027e-141

   1. Initial program 98.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 74.4%

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

      1. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   7. Taylor expanded in z around 0 74.4%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+110}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -0.0085:\\ \;\;\;\;x + \frac{a \cdot y}{z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-198}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-141}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+43}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 3: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{if}\;z \leq -1.92 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \frac{z - y}{\left(t - z\right) + 1}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+14} \lor \neg \left(z \leq 3.3 \cdot 10^{+19}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- (* a (/ y z)) a))))
   (if (<= z -1.92e+74)
     t_1
     (if (<= z -3.8e+29)
       (* a (/ (- z y) (+ (- t z) 1.0)))
       (if (or (<= z -6.2e+14) (not (<= z 3.3e+19)))
         t_1
         (- x (* a (/ y (+ t 1.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a * (y / z)) - a);
	double tmp;
	if (z <= -1.92e+74) {
		tmp = t_1;
	} else if (z <= -3.8e+29) {
		tmp = a * ((z - y) / ((t - z) + 1.0));
	} else if ((z <= -6.2e+14) || !(z <= 3.3e+19)) {
		tmp = t_1;
	} else {
		tmp = x - (a * (y / (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) :: t_1
    real(8) :: tmp
    t_1 = x + ((a * (y / z)) - a)
    if (z <= (-1.92d+74)) then
        tmp = t_1
    else if (z <= (-3.8d+29)) then
        tmp = a * ((z - y) / ((t - z) + 1.0d0))
    else if ((z <= (-6.2d+14)) .or. (.not. (z <= 3.3d+19))) then
        tmp = t_1
    else
        tmp = x - (a * (y / (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 t_1 = x + ((a * (y / z)) - a);
	double tmp;
	if (z <= -1.92e+74) {
		tmp = t_1;
	} else if (z <= -3.8e+29) {
		tmp = a * ((z - y) / ((t - z) + 1.0));
	} else if ((z <= -6.2e+14) || !(z <= 3.3e+19)) {
		tmp = t_1;
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((a * (y / z)) - a)
	tmp = 0
	if z <= -1.92e+74:
		tmp = t_1
	elif z <= -3.8e+29:
		tmp = a * ((z - y) / ((t - z) + 1.0))
	elif (z <= -6.2e+14) or not (z <= 3.3e+19):
		tmp = t_1
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(a * Float64(y / z)) - a))
	tmp = 0.0
	if (z <= -1.92e+74)
		tmp = t_1;
	elseif (z <= -3.8e+29)
		tmp = Float64(a * Float64(Float64(z - y) / Float64(Float64(t - z) + 1.0)));
	elseif ((z <= -6.2e+14) || !(z <= 3.3e+19))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((a * (y / z)) - a);
	tmp = 0.0;
	if (z <= -1.92e+74)
		tmp = t_1;
	elseif (z <= -3.8e+29)
		tmp = a * ((z - y) / ((t - z) + 1.0));
	elseif ((z <= -6.2e+14) || ~((z <= 3.3e+19)))
		tmp = t_1;
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.92e+74], t$95$1, If[LessEqual[z, -3.8e+29], N[(a * N[(N[(z - y), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -6.2e+14], N[Not[LessEqual[z, 3.3e+19]], $MachinePrecision]], t$95$1, N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.92000000000000002e74 or -3.79999999999999971e29 < z < -6.2e14 or 3.3e19 < z

   1. Initial program 91.2%

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

   2. Taylor expanded in z around inf 81.9%

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

      1. mul-1-neg 81.9%

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

      2. distribute-neg-frac 81.9%

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

   4. Simplified 81.9%

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

   5. Taylor expanded in y around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. unsub-neg 84.6%

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

      3. *-commutative 84.6%

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

      4. associate-/l* 89.0%

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

      5. associate-/r/ 89.8%

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

   7. Simplified 89.8%

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

   if -1.92000000000000002e74 < z < -3.79999999999999971e29

   1. Initial program 91.6%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. associate-*r/ 83.5%

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

      3. div-sub 83.3%

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

      4. distribute-rgt-out-- 83.3%

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

      5. sub-neg 83.3%

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

      6. +-commutative 83.3%

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

      7. distribute-neg-in 83.3%

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

      8. remove-double-neg 83.3%

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

      9. distribute-lft-neg-in 83.3%

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

      10. distribute-rgt-in 83.3%

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

      11. sub-neg 83.3%

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

      12. div-sub 83.5%

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

      13. associate--l+ 83.5%

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

   6. Simplified 83.5%

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

   if -6.2e14 < z < 3.3e19

   1. Initial program 99.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 93.9%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.92 \cdot 10^{+74}:\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \frac{z - y}{\left(t - z\right) + 1}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+14} \lor \neg \left(z \leq 3.3 \cdot 10^{+19}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]

Alternative 4: 72.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -34:\\ \;\;\;\;x + \frac{a \cdot y}{z}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-188}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-58}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{1}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+113)
   (- x a)
   (if (<= z -34.0)
     (+ x (/ (* a y) z))
     (if (<= z -5.8e-188)
       (- x (/ a (/ t y)))
       (if (<= z 2.75e-58) (- x (* a y)) (+ x (/ a (+ (/ 1.0 z) -1.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+113) {
		tmp = x - a;
	} else if (z <= -34.0) {
		tmp = x + ((a * y) / z);
	} else if (z <= -5.8e-188) {
		tmp = x - (a / (t / y));
	} else if (z <= 2.75e-58) {
		tmp = x - (a * y);
	} else {
		tmp = x + (a / ((1.0 / z) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.5d+113)) then
        tmp = x - a
    else if (z <= (-34.0d0)) then
        tmp = x + ((a * y) / z)
    else if (z <= (-5.8d-188)) then
        tmp = x - (a / (t / y))
    else if (z <= 2.75d-58) then
        tmp = x - (a * y)
    else
        tmp = x + (a / ((1.0d0 / z) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+113) {
		tmp = x - a;
	} else if (z <= -34.0) {
		tmp = x + ((a * y) / z);
	} else if (z <= -5.8e-188) {
		tmp = x - (a / (t / y));
	} else if (z <= 2.75e-58) {
		tmp = x - (a * y);
	} else {
		tmp = x + (a / ((1.0 / z) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+113:
		tmp = x - a
	elif z <= -34.0:
		tmp = x + ((a * y) / z)
	elif z <= -5.8e-188:
		tmp = x - (a / (t / y))
	elif z <= 2.75e-58:
		tmp = x - (a * y)
	else:
		tmp = x + (a / ((1.0 / z) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+113)
		tmp = Float64(x - a);
	elseif (z <= -34.0)
		tmp = Float64(x + Float64(Float64(a * y) / z));
	elseif (z <= -5.8e-188)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (z <= 2.75e-58)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 / z) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e+113)
		tmp = x - a;
	elseif (z <= -34.0)
		tmp = x + ((a * y) / z);
	elseif (z <= -5.8e-188)
		tmp = x - (a / (t / y));
	elseif (z <= 2.75e-58)
		tmp = x - (a * y);
	else
		tmp = x + (a / ((1.0 / z) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+113], N[(x - a), $MachinePrecision], If[LessEqual[z, -34.0], N[(x + N[(N[(a * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e-188], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.75e-58], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(a / N[(N[(1.0 / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.5000000000000001e113

   1. Initial program 94.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 89.1%

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

   if -8.5000000000000001e113 < z < -34

   1. Initial program 92.0%

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

   2. Taylor expanded in z around inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. distribute-neg-frac 69.7%

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

   4. Simplified 69.7%

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

   5. Taylor expanded in y around inf 64.8%

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

      1. associate-*r/ 64.8%

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

      2. *-commutative 64.8%

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

      3. mul-1-neg 64.8%

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

      4. distribute-rgt-neg-in 64.8%

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

   7. Simplified 64.8%

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

   if -34 < z < -5.8000000000000003e-188

   1. Initial program 99.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 61.9%

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

      1. associate-/l* 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in y around inf 78.4%

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

   if -5.8000000000000003e-188 < z < 2.74999999999999998e-58

   1. Initial program 98.6%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 71.2%

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

      1. associate-/l* 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in z around 0 72.2%

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

   if 2.74999999999999998e-58 < 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%

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

   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 66.2%

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

      1. associate-/l* 81.7%

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

   6. Simplified 81.7%

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

   7. Taylor expanded in y around 0 65.2%

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

      1. sub-neg 65.2%

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

      2. mul-1-neg 65.2%

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

      3. remove-double-neg 65.2%

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

      4. associate-/l* 79.5%

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

      5. div-sub 79.5%

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

      6. sub-neg 79.5%

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

      7. *-inverses 79.5%

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

      8. metadata-eval 79.5%

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

   9. Simplified 79.5%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+113}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -34:\\ \;\;\;\;x + \frac{a \cdot y}{z}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-188}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-58}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{1}{z} + -1}\\ \end{array} \]

Alternative 5: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+110}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{a \cdot y}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+43}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+110)
   (- x a)
   (if (<= z -7.5e+73)
     (+ x (/ (* a y) z))
     (if (<= z -3.8e+29)
       (* a (/ (- z y) t))
       (if (<= z 6.6e+43) (- 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 <= -5.5e+110) {
		tmp = x - a;
	} else if (z <= -7.5e+73) {
		tmp = x + ((a * y) / z);
	} else if (z <= -3.8e+29) {
		tmp = a * ((z - y) / t);
	} else if (z <= 6.6e+43) {
		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 <= (-5.5d+110)) then
        tmp = x - a
    else if (z <= (-7.5d+73)) then
        tmp = x + ((a * y) / z)
    else if (z <= (-3.8d+29)) then
        tmp = a * ((z - y) / t)
    else if (z <= 6.6d+43) 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 <= -5.5e+110) {
		tmp = x - a;
	} else if (z <= -7.5e+73) {
		tmp = x + ((a * y) / z);
	} else if (z <= -3.8e+29) {
		tmp = a * ((z - y) / t);
	} else if (z <= 6.6e+43) {
		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 <= -5.5e+110:
		tmp = x - a
	elif z <= -7.5e+73:
		tmp = x + ((a * y) / z)
	elif z <= -3.8e+29:
		tmp = a * ((z - y) / t)
	elif z <= 6.6e+43:
		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 <= -5.5e+110)
		tmp = Float64(x - a);
	elseif (z <= -7.5e+73)
		tmp = Float64(x + Float64(Float64(a * y) / z));
	elseif (z <= -3.8e+29)
		tmp = Float64(a * Float64(Float64(z - y) / t));
	elseif (z <= 6.6e+43)
		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 <= -5.5e+110)
		tmp = x - a;
	elseif (z <= -7.5e+73)
		tmp = x + ((a * y) / z);
	elseif (z <= -3.8e+29)
		tmp = a * ((z - y) / t);
	elseif (z <= 6.6e+43)
		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, -5.5e+110], N[(x - a), $MachinePrecision], If[LessEqual[z, -7.5e+73], N[(x + N[(N[(a * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e+29], N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+43], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.49999999999999996e110 or 6.6000000000000003e43 < z

   1. Initial program 90.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 87.5%

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

   if -5.49999999999999996e110 < z < -7.5e73

   1. Initial program 90.2%

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

   2. Taylor expanded in z around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. distribute-neg-frac 90.2%

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

   4. Simplified 90.2%

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

   5. Taylor expanded in y around inf 90.7%

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

      1. associate-*r/ 90.7%

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

      2. *-commutative 90.7%

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

      3. mul-1-neg 90.7%

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

      4. distribute-rgt-neg-in 90.7%

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

   7. Simplified 90.7%

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

   if -7.5e73 < z < -3.79999999999999971e29

   1. Initial program 89.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 44.8%

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

      1. associate-/l* 73.0%

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

   6. Simplified 73.0%

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

   7. Taylor expanded in a around inf 53.1%

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

   8. Taylor expanded in z around 0 53.1%

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

      1. neg-mul-1 53.1%

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

      2. unsub-neg 53.1%

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

      3. div-sub 53.2%

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

   10. Simplified 53.2%

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

   if -3.79999999999999971e29 < z < 6.6000000000000003e43

   1. Initial program 99.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 92.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+110}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{a \cdot y}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+29}:\\ \;\;\;\;a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+43}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 6: 70.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+124}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-142}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ a (/ t y)))))
   (if (<= z -8.5e+124)
     (- x a)
     (if (<= z -1.95e-199)
       t_1
       (if (<= z 1.28e-142) (- x (* a y)) (if (<= z 4.1e+40) 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 tmp;
	if (z <= -8.5e+124) {
		tmp = x - a;
	} else if (z <= -1.95e-199) {
		tmp = t_1;
	} else if (z <= 1.28e-142) {
		tmp = x - (a * y);
	} else if (z <= 4.1e+40) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (a / (t / y))
    if (z <= (-8.5d+124)) then
        tmp = x - a
    else if (z <= (-1.95d-199)) then
        tmp = t_1
    else if (z <= 1.28d-142) then
        tmp = x - (a * y)
    else if (z <= 4.1d+40) 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 tmp;
	if (z <= -8.5e+124) {
		tmp = x - a;
	} else if (z <= -1.95e-199) {
		tmp = t_1;
	} else if (z <= 1.28e-142) {
		tmp = x - (a * y);
	} else if (z <= 4.1e+40) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a / (t / y))
	tmp = 0
	if z <= -8.5e+124:
		tmp = x - a
	elif z <= -1.95e-199:
		tmp = t_1
	elif z <= 1.28e-142:
		tmp = x - (a * y)
	elif z <= 4.1e+40:
		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)))
	tmp = 0.0
	if (z <= -8.5e+124)
		tmp = Float64(x - a);
	elseif (z <= -1.95e-199)
		tmp = t_1;
	elseif (z <= 1.28e-142)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 4.1e+40)
		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));
	tmp = 0.0;
	if (z <= -8.5e+124)
		tmp = x - a;
	elseif (z <= -1.95e-199)
		tmp = t_1;
	elseif (z <= 1.28e-142)
		tmp = x - (a * y);
	elseif (z <= 4.1e+40)
		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]}, If[LessEqual[z, -8.5e+124], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.95e-199], t$95$1, If[LessEqual[z, 1.28e-142], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+40], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999997e124 or 4.1000000000000002e40 < z

   1. Initial program 90.8%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 88.3%

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

   if -8.4999999999999997e124 < z < -1.9500000000000001e-199 or 1.2799999999999999e-142 < z < 4.1000000000000002e40

   1. Initial program 97.6%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 52.8%

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

      1. associate-/l* 65.1%

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

   6. Simplified 65.1%

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

   7. Taylor expanded in y around inf 64.3%

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

   if -1.9500000000000001e-199 < z < 1.2799999999999999e-142

   1. Initial program 98.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 74.4%

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

      1. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   7. Taylor expanded in z around 0 74.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+124}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-199}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-142}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+40}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 7: 91.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+48} \lor \neg \left(t \leq 2.8 \cdot 10^{+96}\right):\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.2e+48) (not (<= t 2.8e+96)))
   (- x (/ a (/ t (- y z))))
   (- x (/ a (/ (- 1.0 z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.2e+48) || !(t <= 2.8e+96)) {
		tmp = x - (a / (t / (y - z)));
	} else {
		tmp = x - (a / ((1.0 - z) / (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-6.2d+48)) .or. (.not. (t <= 2.8d+96))) then
        tmp = x - (a / (t / (y - z)))
    else
        tmp = x - (a / ((1.0d0 - z) / (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.2e+48) || !(t <= 2.8e+96)) {
		tmp = x - (a / (t / (y - z)));
	} else {
		tmp = x - (a / ((1.0 - z) / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.2e+48) or not (t <= 2.8e+96):
		tmp = x - (a / (t / (y - z)))
	else:
		tmp = x - (a / ((1.0 - z) / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.2e+48) || !(t <= 2.8e+96))
		tmp = Float64(x - Float64(a / Float64(t / Float64(y - z))));
	else
		tmp = Float64(x - Float64(a / Float64(Float64(1.0 - z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.2e+48) || ~((t <= 2.8e+96)))
		tmp = x - (a / (t / (y - z)));
	else
		tmp = x - (a / ((1.0 - z) / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.2e+48], N[Not[LessEqual[t, 2.8e+96]], $MachinePrecision]], N[(x - N[(a / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(N[(1.0 - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.20000000000000011e48 or 2.8e96 < t

   1. Initial program 95.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 67.0%

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

      1. associate-/l* 86.8%

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

   6. Simplified 86.8%

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

   if -6.20000000000000011e48 < t < 2.8e96

   1. Initial program 94.7%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 84.1%

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

      1. associate-/l* 95.4%

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

   6. Simplified 95.4%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+48} \lor \neg \left(t \leq 2.8 \cdot 10^{+96}\right):\\ \;\;\;\;x - \frac{a}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y - z}}\\ \end{array} \]

Alternative 8: 88.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+18} \lor \neg \left(z \leq 8.2 \cdot 10^{+19}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.14e+18) (not (<= z 8.2e+19)))
   (+ x (- (* a (/ y z)) a))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.14e+18) || !(z <= 8.2e+19)) {
		tmp = x + ((a * (y / z)) - a);
	} else {
		tmp = x - (a * (y / (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 <= (-1.14d+18)) .or. (.not. (z <= 8.2d+19))) then
        tmp = x + ((a * (y / z)) - a)
    else
        tmp = x - (a * (y / (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 <= -1.14e+18) || !(z <= 8.2e+19)) {
		tmp = x + ((a * (y / z)) - a);
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.14e+18) or not (z <= 8.2e+19):
		tmp = x + ((a * (y / z)) - a)
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.14e+18) || !(z <= 8.2e+19))
		tmp = Float64(x + Float64(Float64(a * Float64(y / z)) - a));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.14e+18) || ~((z <= 8.2e+19)))
		tmp = x + ((a * (y / z)) - a);
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.14e+18], N[Not[LessEqual[z, 8.2e+19]], $MachinePrecision]], N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14e18 or 8.2e19 < z

   1. Initial program 91.2%

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

   2. Taylor expanded in z around inf 78.5%

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

      1. mul-1-neg 78.5%

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

      2. distribute-neg-frac 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in y around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. unsub-neg 81.0%

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

      3. *-commutative 81.0%

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

      4. associate-/l* 85.0%

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

      5. associate-/r/ 85.8%

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

   7. Simplified 85.8%

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

   if -1.14e18 < z < 8.2e19

   1. Initial program 99.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 93.9%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+18} \lor \neg \left(z \leq 8.2 \cdot 10^{+19}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]

Alternative 9: 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 95.0%

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

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 10: 63.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+37}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-261}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 0.0082:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+37)
   (- x a)
   (if (<= z -4.4e-261)
     x
     (if (<= z 1.05e-250) (* a (- y)) (if (<= z 0.0082) x (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+37) {
		tmp = x - a;
	} else if (z <= -4.4e-261) {
		tmp = x;
	} else if (z <= 1.05e-250) {
		tmp = a * -y;
	} else if (z <= 0.0082) {
		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 <= (-4.5d+37)) then
        tmp = x - a
    else if (z <= (-4.4d-261)) then
        tmp = x
    else if (z <= 1.05d-250) then
        tmp = a * -y
    else if (z <= 0.0082d0) 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 <= -4.5e+37) {
		tmp = x - a;
	} else if (z <= -4.4e-261) {
		tmp = x;
	} else if (z <= 1.05e-250) {
		tmp = a * -y;
	} else if (z <= 0.0082) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+37:
		tmp = x - a
	elif z <= -4.4e-261:
		tmp = x
	elif z <= 1.05e-250:
		tmp = a * -y
	elif z <= 0.0082:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+37)
		tmp = Float64(x - a);
	elseif (z <= -4.4e-261)
		tmp = x;
	elseif (z <= 1.05e-250)
		tmp = Float64(a * Float64(-y));
	elseif (z <= 0.0082)
		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 <= -4.5e+37)
		tmp = x - a;
	elseif (z <= -4.4e-261)
		tmp = x;
	elseif (z <= 1.05e-250)
		tmp = a * -y;
	elseif (z <= 0.0082)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+37], N[(x - a), $MachinePrecision], If[LessEqual[z, -4.4e-261], x, If[LessEqual[z, 1.05e-250], N[(a * (-y)), $MachinePrecision], If[LessEqual[z, 0.0082], x, N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.49999999999999962e37 or 0.00820000000000000069 < z

   1. Initial program 91.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 78.9%

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

   if -4.49999999999999962e37 < z < -4.4000000000000003e-261 or 1.05e-250 < z < 0.00820000000000000069

   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 x around inf 55.6%

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

   if -4.4000000000000003e-261 < z < 1.05e-250

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 71.3%

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

      1. associate-/l* 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in x around 0 59.8%

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

      1. mul-1-neg 59.8%

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

      2. associate-*l/ 59.8%

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

      3. *-commutative 59.8%

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

      4. distribute-rgt-neg-in 59.8%

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

   9. Simplified 59.8%

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

   10. Taylor expanded in z around 0 59.8%

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

       1. associate-*r* 59.8%

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

       2. mul-1-neg 59.8%

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

   12. Simplified 59.8%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+37}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-261}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 0.0082:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 11: 73.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+37} \lor \neg \left(z \leq 1.3 \cdot 10^{-7}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6e+37) (not (<= z 1.3e-7))) (- x a) (- x (* a y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6e+37) || !(z <= 1.3e-7)) {
		tmp = x - a;
	} else {
		tmp = x - (a * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6d+37)) .or. (.not. (z <= 1.3d-7))) then
        tmp = x - a
    else
        tmp = x - (a * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6e+37) || !(z <= 1.3e-7)) {
		tmp = x - a;
	} else {
		tmp = x - (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6e+37) or not (z <= 1.3e-7):
		tmp = x - a
	else:
		tmp = x - (a * y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6e+37) || !(z <= 1.3e-7))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6e+37) || ~((z <= 1.3e-7)))
		tmp = x - a;
	else
		tmp = x - (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6e+37], N[Not[LessEqual[z, 1.3e-7]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000043e37 or 1.29999999999999999e-7 < z

   1. Initial program 91.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 78.3%

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

   if -6.00000000000000043e37 < z < 1.29999999999999999e-7

   1. Initial program 99.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 69.8%

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

      1. associate-/l* 69.7%

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

   6. Simplified 69.7%

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

   7. Taylor expanded in z around 0 65.0%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+37} \lor \neg \left(z \leq 1.3 \cdot 10^{-7}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \]

Alternative 12: 65.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+37}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 0.049:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+37) (- x a) (if (<= z 0.049) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+37) {
		tmp = x - a;
	} else if (z <= 0.049) {
		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 <= (-4.5d+37)) then
        tmp = x - a
    else if (z <= 0.049d0) 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 <= -4.5e+37) {
		tmp = x - a;
	} else if (z <= 0.049) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+37:
		tmp = x - a
	elif z <= 0.049:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+37)
		tmp = Float64(x - a);
	elseif (z <= 0.049)
		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 <= -4.5e+37)
		tmp = x - a;
	elseif (z <= 0.049)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+37], N[(x - a), $MachinePrecision], If[LessEqual[z, 0.049], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999962e37 or 0.049000000000000002 < z

   1. Initial program 91.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 78.9%

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

   if -4.49999999999999962e37 < z < 0.049000000000000002

   1. Initial program 99.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 51.6%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+37}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 0.049:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 13: 53.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+60}:\\ \;\;\;\;-a\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.4e+60) (- a) (if (<= a 2.3e+153) x (- a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.4e+60) {
		tmp = -a;
	} else if (a <= 2.3e+153) {
		tmp = x;
	} else {
		tmp = -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 (a <= (-5.4d+60)) then
        tmp = -a
    else if (a <= 2.3d+153) then
        tmp = x
    else
        tmp = -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 (a <= -5.4e+60) {
		tmp = -a;
	} else if (a <= 2.3e+153) {
		tmp = x;
	} else {
		tmp = -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.4e+60:
		tmp = -a
	elif a <= 2.3e+153:
		tmp = x
	else:
		tmp = -a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.4e+60)
		tmp = Float64(-a);
	elseif (a <= 2.3e+153)
		tmp = x;
	else
		tmp = Float64(-a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.4e+60)
		tmp = -a;
	elseif (a <= 2.3e+153)
		tmp = x;
	else
		tmp = -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.4e+60], (-a), If[LessEqual[a, 2.3e+153], x, (-a)]]

Derivation

1. Split input into 2 regimes

2. if a < -5.3999999999999999e60 or 2.3000000000000001e153 < a

   1. Initial program 99.7%

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

      1. associate-/r/ 99.9%

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

   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 34.0%

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

      1. associate-/l* 58.3%

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

   6. Simplified 58.3%

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

   7. Taylor expanded in x around 0 30.6%

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

      1. mul-1-neg 30.6%

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

      2. associate-*l/ 54.8%

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

      3. *-commutative 54.8%

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

      4. distribute-rgt-neg-in 54.8%

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

   9. Simplified 54.8%

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

   10. Taylor expanded in z around inf 31.6%

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

       1. mul-1-neg 31.6%

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

   12. Simplified 31.6%

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

   if -5.3999999999999999e60 < a < 2.3000000000000001e153

   1. Initial program 92.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 x around inf 64.5%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+60}:\\ \;\;\;\;-a\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-a\\ \end{array} \]

Alternative 14: 53.5% 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 95.0%

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

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around inf 48.4%

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

5. Final simplification 48.4%

   \[\leadsto x \]

Developer target: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023192 
(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))))