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

Percentage Accurate: 97.2% → 99.7%

Time: 19.7s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.2% 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: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

   1. associate-/r/ 99.6%

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

   2. *-commutative 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+143}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -14800000:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-24} \lor \neg \left(z \leq 640\right):\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e+143)
   (- x a)
   (if (<= z -14800000.0)
     (+ x (/ a (/ z y)))
     (if (or (<= z -5.8e-24) (not (<= z 640.0)))
       (+ x (/ a (/ (- 1.0 z) z)))
       (- x (* a (/ y (+ t 1.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+143) {
		tmp = x - a;
	} else if (z <= -14800000.0) {
		tmp = x + (a / (z / y));
	} else if ((z <= -5.8e-24) || !(z <= 640.0)) {
		tmp = x + (a / ((1.0 - z) / z));
	} 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 <= (-9.2d+143)) then
        tmp = x - a
    else if (z <= (-14800000.0d0)) then
        tmp = x + (a / (z / y))
    else if ((z <= (-5.8d-24)) .or. (.not. (z <= 640.0d0))) then
        tmp = x + (a / ((1.0d0 - z) / z))
    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 <= -9.2e+143) {
		tmp = x - a;
	} else if (z <= -14800000.0) {
		tmp = x + (a / (z / y));
	} else if ((z <= -5.8e-24) || !(z <= 640.0)) {
		tmp = x + (a / ((1.0 - z) / z));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e+143:
		tmp = x - a
	elif z <= -14800000.0:
		tmp = x + (a / (z / y))
	elif (z <= -5.8e-24) or not (z <= 640.0):
		tmp = x + (a / ((1.0 - z) / z))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+143)
		tmp = Float64(x - a);
	elseif (z <= -14800000.0)
		tmp = Float64(x + Float64(a / Float64(z / y)));
	elseif ((z <= -5.8e-24) || !(z <= 640.0))
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 - z) / z)));
	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 <= -9.2e+143)
		tmp = x - a;
	elseif (z <= -14800000.0)
		tmp = x + (a / (z / y));
	elseif ((z <= -5.8e-24) || ~((z <= 640.0)))
		tmp = x + (a / ((1.0 - z) / z));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+143], N[(x - a), $MachinePrecision], If[LessEqual[z, -14800000.0], N[(x + N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -5.8e-24], N[Not[LessEqual[z, 640.0]], $MachinePrecision]], N[(x + N[(a / N[(N[(1.0 - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.1999999999999999e143

   1. Initial program 87.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 79.8%

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

   if -9.1999999999999999e143 < z < -1.48e7

   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%

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

      2. *-commutative 99.9%

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

      3. associate-*r/ 91.8%

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

      4. div-inv 91.8%

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

   3. Applied egg-rr 91.8%

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

   4. Taylor expanded in y around inf 86.1%

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

   5. Taylor expanded in z around inf 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-/l* 79.8%

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

   7. Simplified 79.8%

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

   if -1.48e7 < z < -5.7999999999999997e-24 or 640 < z

   1. Initial program 95.9%

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

      1. associate-/r/ 99.9%

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

      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 60.1%

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

      1. associate-/l* 95.0%

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

   6. Simplified 95.0%

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

   7. Taylor expanded in y around 0 54.7%

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

      1. sub-neg 54.7%

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

      2. mul-1-neg 54.7%

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

      3. remove-double-neg 54.7%

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

      4. associate-/l* 87.0%

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

   9. Simplified 87.0%

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

   if -5.7999999999999997e-24 < z < 640

   1. Initial program 99.0%

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

      1. associate-/r/ 99.4%

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

      2. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 95.3%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+143}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -14800000:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-24} \lor \neg \left(z \leq 640\right):\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]

Alternative 3: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+144}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -15000000000:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-23} \lor \neg \left(z \leq 105\right):\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.06e+144)
   (- x a)
   (if (<= z -15000000000.0)
     (- x (/ a (/ (- 1.0 z) y)))
     (if (or (<= z -1.8e-23) (not (<= z 105.0)))
       (+ x (/ a (/ (- 1.0 z) z)))
       (- x (* a (/ y (+ t 1.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.06e+144) {
		tmp = x - a;
	} else if (z <= -15000000000.0) {
		tmp = x - (a / ((1.0 - z) / y));
	} else if ((z <= -1.8e-23) || !(z <= 105.0)) {
		tmp = x + (a / ((1.0 - z) / z));
	} 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 <= (-1.06d+144)) then
        tmp = x - a
    else if (z <= (-15000000000.0d0)) then
        tmp = x - (a / ((1.0d0 - z) / y))
    else if ((z <= (-1.8d-23)) .or. (.not. (z <= 105.0d0))) then
        tmp = x + (a / ((1.0d0 - z) / z))
    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 <= -1.06e+144) {
		tmp = x - a;
	} else if (z <= -15000000000.0) {
		tmp = x - (a / ((1.0 - z) / y));
	} else if ((z <= -1.8e-23) || !(z <= 105.0)) {
		tmp = x + (a / ((1.0 - z) / z));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.06e+144:
		tmp = x - a
	elif z <= -15000000000.0:
		tmp = x - (a / ((1.0 - z) / y))
	elif (z <= -1.8e-23) or not (z <= 105.0):
		tmp = x + (a / ((1.0 - z) / z))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.06e+144)
		tmp = Float64(x - a);
	elseif (z <= -15000000000.0)
		tmp = Float64(x - Float64(a / Float64(Float64(1.0 - z) / y)));
	elseif ((z <= -1.8e-23) || !(z <= 105.0))
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 - z) / z)));
	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 <= -1.06e+144)
		tmp = x - a;
	elseif (z <= -15000000000.0)
		tmp = x - (a / ((1.0 - z) / y));
	elseif ((z <= -1.8e-23) || ~((z <= 105.0)))
		tmp = x + (a / ((1.0 - z) / z));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.06e+144], N[(x - a), $MachinePrecision], If[LessEqual[z, -15000000000.0], N[(x - N[(a / N[(N[(1.0 - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.8e-23], N[Not[LessEqual[z, 105.0]], $MachinePrecision]], N[(x + N[(a / N[(N[(1.0 - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.06e144

   1. Initial program 87.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 79.8%

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

   if -1.06e144 < z < -1.5e10

   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%

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

      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 78.5%

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

      1. associate-/l* 83.8%

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

   6. Simplified 83.8%

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

   7. Taylor expanded in y around inf 77.9%

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

      1. associate-/l* 80.6%

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

   9. Simplified 80.6%

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

   if -1.5e10 < z < -1.7999999999999999e-23 or 105 < z

   1. Initial program 95.9%

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

      1. associate-/r/ 99.9%

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

      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 60.1%

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

      1. associate-/l* 95.0%

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

   6. Simplified 95.0%

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

   7. Taylor expanded in y around 0 54.7%

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

      1. sub-neg 54.7%

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

      2. mul-1-neg 54.7%

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

      3. remove-double-neg 54.7%

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

      4. associate-/l* 87.0%

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

   9. Simplified 87.0%

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

   if -1.7999999999999999e-23 < z < 105

   1. Initial program 99.0%

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

      1. associate-/r/ 99.4%

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

      2. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 95.3%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+144}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -15000000000:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-23} \lor \neg \left(z \leq 105\right):\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]

Alternative 4: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot y\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+143}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-239}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 78:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a y))))
   (if (<= z -8.5e+143)
     (- x a)
     (if (<= z -6e-17)
       (+ x (/ a (/ z y)))
       (if (<= z -5.8e-178)
         t_1
         (if (<= z -6.5e-239)
           (- x (/ a (/ t y)))
           (if (<= z 78.0) t_1 (- x a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * y);
	double tmp;
	if (z <= -8.5e+143) {
		tmp = x - a;
	} else if (z <= -6e-17) {
		tmp = x + (a / (z / y));
	} else if (z <= -5.8e-178) {
		tmp = t_1;
	} else if (z <= -6.5e-239) {
		tmp = x - (a / (t / y));
	} else if (z <= 78.0) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (a * y)
    if (z <= (-8.5d+143)) then
        tmp = x - a
    else if (z <= (-6d-17)) then
        tmp = x + (a / (z / y))
    else if (z <= (-5.8d-178)) then
        tmp = t_1
    else if (z <= (-6.5d-239)) then
        tmp = x - (a / (t / y))
    else if (z <= 78.0d0) then
        tmp = t_1
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * y);
	double tmp;
	if (z <= -8.5e+143) {
		tmp = x - a;
	} else if (z <= -6e-17) {
		tmp = x + (a / (z / y));
	} else if (z <= -5.8e-178) {
		tmp = t_1;
	} else if (z <= -6.5e-239) {
		tmp = x - (a / (t / y));
	} else if (z <= 78.0) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * y)
	tmp = 0
	if z <= -8.5e+143:
		tmp = x - a
	elif z <= -6e-17:
		tmp = x + (a / (z / y))
	elif z <= -5.8e-178:
		tmp = t_1
	elif z <= -6.5e-239:
		tmp = x - (a / (t / y))
	elif z <= 78.0:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * y))
	tmp = 0.0
	if (z <= -8.5e+143)
		tmp = Float64(x - a);
	elseif (z <= -6e-17)
		tmp = Float64(x + Float64(a / Float64(z / y)));
	elseif (z <= -5.8e-178)
		tmp = t_1;
	elseif (z <= -6.5e-239)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (z <= 78.0)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * y);
	tmp = 0.0;
	if (z <= -8.5e+143)
		tmp = x - a;
	elseif (z <= -6e-17)
		tmp = x + (a / (z / y));
	elseif (z <= -5.8e-178)
		tmp = t_1;
	elseif (z <= -6.5e-239)
		tmp = x - (a / (t / y));
	elseif (z <= 78.0)
		tmp = t_1;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+143], N[(x - a), $MachinePrecision], If[LessEqual[z, -6e-17], N[(x + N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e-178], t$95$1, If[LessEqual[z, -6.5e-239], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 78.0], t$95$1, N[(x - a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.4999999999999998e143 or 78 < z

   1. Initial program 93.1%

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

      1. associate-/r/ 99.9%

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

      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 83.7%

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

   if -8.4999999999999998e143 < z < -6.00000000000000012e-17

   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%

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

      2. *-commutative 99.9%

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

      3. associate-*r/ 92.6%

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

      4. div-inv 92.6%

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

   3. Applied egg-rr 92.6%

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

   4. Taylor expanded in y around inf 85.1%

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

   5. Taylor expanded in z around inf 77.0%

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

      1. +-commutative 77.0%

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

      2. associate-/l* 79.4%

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

   7. Simplified 79.4%

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

   if -6.00000000000000012e-17 < z < -5.7999999999999995e-178 or -6.5000000000000003e-239 < z < 78

   1. Initial program 98.9%

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

      1. associate-/r/ 99.3%

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

      2. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in t around 0 77.0%

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

      1. associate-/l* 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in z around 0 72.8%

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

   if -5.7999999999999995e-178 < z < -6.5000000000000003e-239

   1. Initial program 99.7%

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

      1. associate-/r/ 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around inf 74.2%

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

      1. associate-/l* 91.3%

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

   6. Simplified 91.3%

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

   7. Taylor expanded in y around inf 73.7%

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

      1. associate-/l* 90.7%

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

   9. Simplified 90.7%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+143}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-178}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-239}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 78:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 5: 92.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+51} \lor \neg \left(z \leq 200\right):\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{t + 1}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e+51) (not (<= z 200.0)))
   (- x (/ a (/ (- 1.0 z) (- y z))))
   (+ x (/ (- z y) (/ (+ t 1.0) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+51) || !(z <= 200.0)) {
		tmp = x - (a / ((1.0 - z) / (y - z)));
	} else {
		tmp = x + ((z - y) / ((t + 1.0) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8d+51)) .or. (.not. (z <= 200.0d0))) then
        tmp = x - (a / ((1.0d0 - z) / (y - z)))
    else
        tmp = x + ((z - y) / ((t + 1.0d0) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+51) || !(z <= 200.0)) {
		tmp = x - (a / ((1.0 - z) / (y - z)));
	} else {
		tmp = x + ((z - y) / ((t + 1.0) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e+51) or not (z <= 200.0):
		tmp = x - (a / ((1.0 - z) / (y - z)))
	else:
		tmp = x + ((z - y) / ((t + 1.0) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e+51) || !(z <= 200.0))
		tmp = Float64(x - Float64(a / Float64(Float64(1.0 - z) / Float64(y - z))));
	else
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(t + 1.0) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8e+51) || ~((z <= 200.0)))
		tmp = x - (a / ((1.0 - z) / (y - z)));
	else
		tmp = x + ((z - y) / ((t + 1.0) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e+51], N[Not[LessEqual[z, 200.0]], $MachinePrecision]], N[(x - N[(a / N[(N[(1.0 - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - y), $MachinePrecision] / N[(N[(t + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8e51 or 200 < z

   1. Initial program 94.2%

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

      1. associate-/r/ 99.9%

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

      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 59.4%

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

      1. associate-/l* 92.4%

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

   6. Simplified 92.4%

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

   if -8e51 < z < 200

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 97.7%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+51} \lor \neg \left(z \leq 200\right):\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{t + 1}{a}}\\ \end{array} \]

Alternative 6: 90.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+150}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+60}:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.1e+150)
   (- x (* a (/ y (+ t 1.0))))
   (if (<= t 1.3e+60)
     (- x (/ a (/ (- 1.0 z) (- y z))))
     (+ x (* a (/ (- z y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e+150) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (t <= 1.3e+60) {
		tmp = x - (a / ((1.0 - z) / (y - 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 <= (-1.1d+150)) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else if (t <= 1.3d+60) then
        tmp = x - (a / ((1.0d0 - z) / (y - 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 <= -1.1e+150) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (t <= 1.3e+60) {
		tmp = x - (a / ((1.0 - z) / (y - z)));
	} else {
		tmp = x + (a * ((z - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.1e+150:
		tmp = x - (a * (y / (t + 1.0)))
	elif t <= 1.3e+60:
		tmp = x - (a / ((1.0 - z) / (y - z)))
	else:
		tmp = x + (a * ((z - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.1e+150)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	elseif (t <= 1.3e+60)
		tmp = Float64(x - Float64(a / Float64(Float64(1.0 - z) / Float64(y - 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 <= -1.1e+150)
		tmp = x - (a * (y / (t + 1.0)));
	elseif (t <= 1.3e+60)
		tmp = x - (a / ((1.0 - z) / (y - z)));
	else
		tmp = x + (a * ((z - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.1e+150], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+60], N[(x - N[(a / N[(N[(1.0 - z), $MachinePrecision] / N[(y - 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 < -1.1e150

   1. Initial program 88.1%

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

      1. associate-/r/ 99.8%

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

      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 z around 0 94.9%

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

   if -1.1e150 < t < 1.30000000000000004e60

   1. Initial program 98.2%

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

      1. associate-/r/ 99.9%

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

      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 77.9%

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

      1. associate-/l* 96.5%

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

   6. Simplified 96.5%

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

   if 1.30000000000000004e60 < t

   1. Initial program 97.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 84.6%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+150}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+60}:\\ \;\;\;\;x - \frac{a}{\frac{1 - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]

Alternative 7: 87.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+52} \lor \neg \left(z \leq 900\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.6e+52) (not (<= z 900.0)))
   (+ x (/ (- z 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 <= -4.6e+52) || !(z <= 900.0)) {
		tmp = x + ((z - 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 <= (-4.6d+52)) .or. (.not. (z <= 900.0d0))) then
        tmp = x + ((z - 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 <= -4.6e+52) || !(z <= 900.0)) {
		tmp = x + ((z - 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 <= -4.6e+52) or not (z <= 900.0):
		tmp = x + ((z - 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 <= -4.6e+52) || !(z <= 900.0))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(-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 <= -4.6e+52) || ~((z <= 900.0)))
		tmp = x + ((z - 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, -4.6e+52], N[Not[LessEqual[z, 900.0]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $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 < -4.6e52 or 900 < z

   1. Initial program 94.2%

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

   2. Taylor expanded in z around inf 90.4%

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

      1. mul-1-neg 90.4%

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

      2. distribute-neg-frac 90.4%

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

   4. Simplified 90.4%

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

   if -4.6e52 < z < 900

   1. Initial program 99.1%

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

      1. associate-/r/ 99.4%

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

      2. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 92.2%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+52} \lor \neg \left(z \leq 900\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]

Alternative 8: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+156} \lor \neg \left(t \leq 1.65 \cdot 10^{+16}\right):\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.7e+156) (not (<= t 1.65e+16)))
   (- x (/ a (/ t y)))
   (+ x (/ a (/ (- 1.0 z) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.7e+156) || !(t <= 1.65e+16)) {
		tmp = x - (a / (t / y));
	} else {
		tmp = x + (a / ((1.0 - z) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.7d+156)) .or. (.not. (t <= 1.65d+16))) then
        tmp = x - (a / (t / y))
    else
        tmp = x + (a / ((1.0d0 - z) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.7e+156) || !(t <= 1.65e+16)) {
		tmp = x - (a / (t / y));
	} else {
		tmp = x + (a / ((1.0 - z) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.7e+156) or not (t <= 1.65e+16):
		tmp = x - (a / (t / y))
	else:
		tmp = x + (a / ((1.0 - z) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.7e+156) || !(t <= 1.65e+16))
		tmp = Float64(x - Float64(a / Float64(t / y)));
	else
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 - z) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.7e+156) || ~((t <= 1.65e+16)))
		tmp = x - (a / (t / y));
	else
		tmp = x + (a / ((1.0 - z) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.7e+156], N[Not[LessEqual[t, 1.65e+16]], $MachinePrecision]], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a / N[(N[(1.0 - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.7e156 or 1.65e16 < t

   1. Initial program 94.2%

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

      1. associate-/r/ 99.1%

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

      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 inf 72.3%

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

      1. associate-/l* 85.2%

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

   6. Simplified 85.2%

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

   7. Taylor expanded in y around inf 75.7%

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

      1. associate-/l* 85.3%

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

   9. Simplified 85.3%

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

   if -1.7e156 < t < 1.65e16

   1. Initial program 98.1%

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

      1. associate-/r/ 99.9%

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

      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 78.2%

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

      1. associate-/l* 96.6%

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

   6. Simplified 96.6%

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

   7. Taylor expanded in y around 0 60.0%

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

      1. sub-neg 60.0%

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

      2. mul-1-neg 60.0%

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

      3. remove-double-neg 60.0%

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

      4. associate-/l* 75.8%

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

   9. Simplified 75.8%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+156} \lor \neg \left(t \leq 1.65 \cdot 10^{+16}\right):\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \end{array} \]

Alternative 9: 73.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+144}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -170000:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 78:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+144)
   (- x a)
   (if (<= z -170000.0)
     (+ x (/ a (/ z y)))
     (if (<= z 78.0) (- x (* a y)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+144) {
		tmp = x - a;
	} else if (z <= -170000.0) {
		tmp = x + (a / (z / y));
	} else if (z <= 78.0) {
		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 <= (-1.05d+144)) then
        tmp = x - a
    else if (z <= (-170000.0d0)) then
        tmp = x + (a / (z / y))
    else if (z <= 78.0d0) 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 <= -1.05e+144) {
		tmp = x - a;
	} else if (z <= -170000.0) {
		tmp = x + (a / (z / y));
	} else if (z <= 78.0) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+144:
		tmp = x - a
	elif z <= -170000.0:
		tmp = x + (a / (z / y))
	elif z <= 78.0:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+144)
		tmp = Float64(x - a);
	elseif (z <= -170000.0)
		tmp = Float64(x + Float64(a / Float64(z / y)));
	elseif (z <= 78.0)
		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 <= -1.05e+144)
		tmp = x - a;
	elseif (z <= -170000.0)
		tmp = x + (a / (z / y));
	elseif (z <= 78.0)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+144], N[(x - a), $MachinePrecision], If[LessEqual[z, -170000.0], N[(x + N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 78.0], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04999999999999998e144 or 78 < z

   1. Initial program 93.1%

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

      1. associate-/r/ 99.9%

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

      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 83.7%

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

   if -1.04999999999999998e144 < z < -1.7e5

   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%

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

      2. *-commutative 99.9%

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

      3. associate-*r/ 91.8%

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

      4. div-inv 91.8%

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

   3. Applied egg-rr 91.8%

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

   4. Taylor expanded in y around inf 86.1%

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

   5. Taylor expanded in z around inf 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-/l* 79.8%

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

   7. Simplified 79.8%

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

   if -1.7e5 < z < 78

   1. Initial program 99.0%

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

      1. associate-/r/ 99.4%

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

      2. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in t around 0 76.0%

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

      1. associate-/l* 75.9%

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

   6. Simplified 75.9%

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

   7. Taylor expanded in z around 0 70.7%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+144}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -170000:\\ \;\;\;\;x + \frac{a}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 78:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 10: 73.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+50} \lor \neg \left(z \leq 55\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.8e+50) (not (<= z 55.0))) (- x a) (- x (* a y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.8e+50) || !(z <= 55.0)) {
		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 <= (-3.8d+50)) .or. (.not. (z <= 55.0d0))) 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 <= -3.8e+50) || !(z <= 55.0)) {
		tmp = x - a;
	} else {
		tmp = x - (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.8e+50) or not (z <= 55.0):
		tmp = x - a
	else:
		tmp = x - (a * y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.8e+50) || !(z <= 55.0))
		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 <= -3.8e+50) || ~((z <= 55.0)))
		tmp = x - a;
	else
		tmp = x - (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.8e+50], N[Not[LessEqual[z, 55.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.79999999999999987e50 or 55 < z

   1. Initial program 94.2%

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

      1. associate-/r/ 99.9%

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

      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 80.3%

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

   if -3.79999999999999987e50 < z < 55

   1. Initial program 99.1%

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

      1. associate-/r/ 99.4%

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

      2. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in t around 0 75.6%

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

      1. associate-/l* 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in z around 0 70.8%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+50} \lor \neg \left(z \leq 55\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \]

Alternative 11: 66.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+50}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e+50) (- x a) (if (<= z 1.95e-73) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+50) {
		tmp = x - a;
	} else if (z <= 1.95e-73) {
		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 <= (-4d+50)) then
        tmp = x - a
    else if (z <= 1.95d-73) 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 <= -4e+50) {
		tmp = x - a;
	} else if (z <= 1.95e-73) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e+50:
		tmp = x - a
	elif z <= 1.95e-73:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e+50)
		tmp = Float64(x - a);
	elseif (z <= 1.95e-73)
		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 <= -4e+50)
		tmp = x - a;
	elseif (z <= 1.95e-73)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e+50], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.95e-73], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0000000000000003e50 or 1.94999999999999991e-73 < z

   1. Initial program 94.8%

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

      1. associate-/r/ 99.9%

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

      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 77.5%

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

   if -4.0000000000000003e50 < z < 1.94999999999999991e-73

   1. Initial program 99.0%

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

      1. associate-/r/ 99.3%

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

      2. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around inf 60.9%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+50}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 12: 54.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

   1. associate-/r/ 99.6%

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

   2. *-commutative 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in x around inf 53.8%

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

5. Final simplification 53.8%

   \[\leadsto x \]

Developer target: 99.7% 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 2023275 
(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))))