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

Percentage Accurate: 97.6% → 99.5%

Time: 12.3s

Alternatives: 18

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: 97.6% 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: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / ((1.0d0 - (z - t)) / (z - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

   1. associate-/r/ 99.8%

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

3. Simplified 99.8%

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

   1. *-commutative 99.8%

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

   2. clear-num 99.8%

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

   3. un-div-inv 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 69.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+168}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-56}:\\ \;\;\;\;x + a \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-91}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-183}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+105}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+168)
   (- x a)
   (if (<= z -5.5e-56)
     (+ x (* a (/ y z)))
     (if (<= z -7.6e-91)
       (- x (* a (/ y t)))
       (if (<= z -6.2e-183)
         (- x (* a y))
         (if (<= z 8.6e+105) (- x (/ a (/ t y))) (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+168) {
		tmp = x - a;
	} else if (z <= -5.5e-56) {
		tmp = x + (a * (y / z));
	} else if (z <= -7.6e-91) {
		tmp = x - (a * (y / t));
	} else if (z <= -6.2e-183) {
		tmp = x - (a * y);
	} else if (z <= 8.6e+105) {
		tmp = x - (a / (t / 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+168)) then
        tmp = x - a
    else if (z <= (-5.5d-56)) then
        tmp = x + (a * (y / z))
    else if (z <= (-7.6d-91)) then
        tmp = x - (a * (y / t))
    else if (z <= (-6.2d-183)) then
        tmp = x - (a * y)
    else if (z <= 8.6d+105) then
        tmp = x - (a / (t / 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+168) {
		tmp = x - a;
	} else if (z <= -5.5e-56) {
		tmp = x + (a * (y / z));
	} else if (z <= -7.6e-91) {
		tmp = x - (a * (y / t));
	} else if (z <= -6.2e-183) {
		tmp = x - (a * y);
	} else if (z <= 8.6e+105) {
		tmp = x - (a / (t / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+168:
		tmp = x - a
	elif z <= -5.5e-56:
		tmp = x + (a * (y / z))
	elif z <= -7.6e-91:
		tmp = x - (a * (y / t))
	elif z <= -6.2e-183:
		tmp = x - (a * y)
	elif z <= 8.6e+105:
		tmp = x - (a / (t / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+168)
		tmp = Float64(x - a);
	elseif (z <= -5.5e-56)
		tmp = Float64(x + Float64(a * Float64(y / z)));
	elseif (z <= -7.6e-91)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= -6.2e-183)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 8.6e+105)
		tmp = Float64(x - Float64(a / Float64(t / 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+168)
		tmp = x - a;
	elseif (z <= -5.5e-56)
		tmp = x + (a * (y / z));
	elseif (z <= -7.6e-91)
		tmp = x - (a * (y / t));
	elseif (z <= -6.2e-183)
		tmp = x - (a * y);
	elseif (z <= 8.6e+105)
		tmp = x - (a / (t / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+168], N[(x - a), $MachinePrecision], If[LessEqual[z, -5.5e-56], N[(x + N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e-91], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-183], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e+105], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.05000000000000001e168 or 8.6000000000000003e105 < z

   1. Initial program 94.1%

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

   5. Taylor expanded in z around inf 92.8%

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

   if -1.05000000000000001e168 < z < -5.4999999999999999e-56

   1. Initial program 97.8%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 72.6%

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

   6. Taylor expanded in z around inf 52.3%

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

      1. associate-*r/ 52.3%

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

      2. *-commutative 52.3%

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

      3. neg-mul-1 52.3%

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

      4. distribute-lft-neg-in 52.3%

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

      5. neg-mul-1 52.3%

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

      6. *-rgt-identity 52.3%

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

      7. times-frac 59.9%

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

      8. neg-mul-1 59.9%

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

      9. /-rgt-identity 59.9%

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

   8. Simplified 59.9%

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

   if -5.4999999999999999e-56 < z < -7.59999999999999957e-91

   1. Initial program 77.0%

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

      1. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 75.6%

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

   6. Taylor expanded in t around inf 75.6%

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

   if -7.59999999999999957e-91 < z < -6.19999999999999999e-183

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 79.6%

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

   4. Taylor expanded in z around 0 74.5%

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

   if -6.19999999999999999e-183 < z < 8.6000000000000003e105

   1. Initial program 98.1%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 91.9%

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

   6. Taylor expanded in t around inf 83.5%

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

      1. *-commutative 83.5%

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

      2. clear-num 83.5%

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

      3. un-div-inv 83.5%

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

   8. Applied egg-rr 83.5%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+168}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-56}:\\ \;\;\;\;x + a \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-91}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-183}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+105}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+25}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{-109}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-121}:\\ \;\;\;\;x + a \cdot \frac{z}{1 - z}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-175}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.1e+25)
   (- x a)
   (if (<= z -3.65e-109)
     (- x (* a (/ y t)))
     (if (<= z -3.5e-121)
       (+ x (* a (/ z (- 1.0 z))))
       (if (<= z -1.35e-175)
         (- x (* a y))
         (if (<= z 2.3e+104) (- x (/ a (/ t y))) (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+25) {
		tmp = x - a;
	} else if (z <= -3.65e-109) {
		tmp = x - (a * (y / t));
	} else if (z <= -3.5e-121) {
		tmp = x + (a * (z / (1.0 - z)));
	} else if (z <= -1.35e-175) {
		tmp = x - (a * y);
	} else if (z <= 2.3e+104) {
		tmp = x - (a / (t / 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 <= (-2.1d+25)) then
        tmp = x - a
    else if (z <= (-3.65d-109)) then
        tmp = x - (a * (y / t))
    else if (z <= (-3.5d-121)) then
        tmp = x + (a * (z / (1.0d0 - z)))
    else if (z <= (-1.35d-175)) then
        tmp = x - (a * y)
    else if (z <= 2.3d+104) then
        tmp = x - (a / (t / 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 <= -2.1e+25) {
		tmp = x - a;
	} else if (z <= -3.65e-109) {
		tmp = x - (a * (y / t));
	} else if (z <= -3.5e-121) {
		tmp = x + (a * (z / (1.0 - z)));
	} else if (z <= -1.35e-175) {
		tmp = x - (a * y);
	} else if (z <= 2.3e+104) {
		tmp = x - (a / (t / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.1e+25:
		tmp = x - a
	elif z <= -3.65e-109:
		tmp = x - (a * (y / t))
	elif z <= -3.5e-121:
		tmp = x + (a * (z / (1.0 - z)))
	elif z <= -1.35e-175:
		tmp = x - (a * y)
	elif z <= 2.3e+104:
		tmp = x - (a / (t / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.1e+25)
		tmp = Float64(x - a);
	elseif (z <= -3.65e-109)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= -3.5e-121)
		tmp = Float64(x + Float64(a * Float64(z / Float64(1.0 - z))));
	elseif (z <= -1.35e-175)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 2.3e+104)
		tmp = Float64(x - Float64(a / Float64(t / 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 <= -2.1e+25)
		tmp = x - a;
	elseif (z <= -3.65e-109)
		tmp = x - (a * (y / t));
	elseif (z <= -3.5e-121)
		tmp = x + (a * (z / (1.0 - z)));
	elseif (z <= -1.35e-175)
		tmp = x - (a * y);
	elseif (z <= 2.3e+104)
		tmp = x - (a / (t / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.1e+25], N[(x - a), $MachinePrecision], If[LessEqual[z, -3.65e-109], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-121], N[(x + N[(a * N[(z / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.35e-175], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+104], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.0999999999999999e25 or 2.29999999999999985e104 < 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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.6%

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

   if -2.0999999999999999e25 < z < -3.6500000000000002e-109

   1. Initial program 90.2%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 81.7%

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

   6. Taylor expanded in t around inf 71.2%

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

   if -3.6500000000000002e-109 < z < -3.49999999999999993e-121

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0 99.5%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. mul-1-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if -3.49999999999999993e-121 < z < -1.34999999999999999e-175

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 84.7%

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

   4. Taylor expanded in z around 0 84.7%

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

   if -1.34999999999999999e-175 < z < 2.29999999999999985e104

   1. Initial program 98.1%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 91.9%

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

   6. Taylor expanded in t around inf 83.5%

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

      1. *-commutative 83.5%

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

      2. clear-num 83.5%

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

      3. un-div-inv 83.5%

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

   8. Applied egg-rr 83.5%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+25}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{-109}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-121}:\\ \;\;\;\;x + a \cdot \frac{z}{1 - z}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-175}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+100}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{+57}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z - y}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+34}:\\ \;\;\;\;x + a \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+105}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+100)
   (- x a)
   (if (<= z -1.32e+57)
     (+ x (/ a (/ t (- z y))))
     (if (<= z -1.55e+34)
       (+ x (* a (/ y z)))
       (if (<= z 9.6e+105) (+ x (* a (/ y (- -1.0 t)))) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+100) {
		tmp = x - a;
	} else if (z <= -1.32e+57) {
		tmp = x + (a / (t / (z - y)));
	} else if (z <= -1.55e+34) {
		tmp = x + (a * (y / z));
	} else if (z <= 9.6e+105) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.45d+100)) then
        tmp = x - a
    else if (z <= (-1.32d+57)) then
        tmp = x + (a / (t / (z - y)))
    else if (z <= (-1.55d+34)) then
        tmp = x + (a * (y / z))
    else if (z <= 9.6d+105) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+100) {
		tmp = x - a;
	} else if (z <= -1.32e+57) {
		tmp = x + (a / (t / (z - y)));
	} else if (z <= -1.55e+34) {
		tmp = x + (a * (y / z));
	} else if (z <= 9.6e+105) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+100:
		tmp = x - a
	elif z <= -1.32e+57:
		tmp = x + (a / (t / (z - y)))
	elif z <= -1.55e+34:
		tmp = x + (a * (y / z))
	elif z <= 9.6e+105:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+100)
		tmp = Float64(x - a);
	elseif (z <= -1.32e+57)
		tmp = Float64(x + Float64(a / Float64(t / Float64(z - y))));
	elseif (z <= -1.55e+34)
		tmp = Float64(x + Float64(a * Float64(y / z)));
	elseif (z <= 9.6e+105)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+100)
		tmp = x - a;
	elseif (z <= -1.32e+57)
		tmp = x + (a / (t / (z - y)));
	elseif (z <= -1.55e+34)
		tmp = x + (a * (y / z));
	elseif (z <= 9.6e+105)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+100], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.32e+57], N[(x + N[(a / N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e+34], N[(x + N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e+105], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.45e100 or 9.599999999999999e105 < 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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 87.6%

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

   if -1.45e100 < z < -1.32000000000000001e57

   1. Initial program 100.0%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around inf 76.8%

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

   if -1.32000000000000001e57 < z < -1.54999999999999989e34

   1. Initial program 99.7%

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

      1. associate-/r/ 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 70.0%

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

   6. Taylor expanded in z around inf 70.4%

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

      1. associate-*r/ 70.4%

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

      2. *-commutative 70.4%

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

      3. neg-mul-1 70.4%

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

      4. distribute-lft-neg-in 70.4%

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

      5. neg-mul-1 70.4%

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

      6. *-rgt-identity 70.4%

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

      7. times-frac 70.4%

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

      8. neg-mul-1 70.4%

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

      9. /-rgt-identity 70.4%

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

   8. Simplified 70.4%

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

   if -1.54999999999999989e34 < z < 9.599999999999999e105

   1. Initial program 97.3%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 86.4%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+100}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{+57}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z - y}}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+34}:\\ \;\;\;\;x + a \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+105}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+100}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+57}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+33}:\\ \;\;\;\;x + a \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+104}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+100)
   (- x a)
   (if (<= z -2.9e+57)
     (+ x (/ (- z y) (/ t a)))
     (if (<= z -3.4e+33)
       (+ x (* a (/ y z)))
       (if (<= z 2.25e+104) (+ x (* a (/ y (- -1.0 t)))) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+100) {
		tmp = x - a;
	} else if (z <= -2.9e+57) {
		tmp = x + ((z - y) / (t / a));
	} else if (z <= -3.4e+33) {
		tmp = x + (a * (y / z));
	} else if (z <= 2.25e+104) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.45d+100)) then
        tmp = x - a
    else if (z <= (-2.9d+57)) then
        tmp = x + ((z - y) / (t / a))
    else if (z <= (-3.4d+33)) then
        tmp = x + (a * (y / z))
    else if (z <= 2.25d+104) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+100) {
		tmp = x - a;
	} else if (z <= -2.9e+57) {
		tmp = x + ((z - y) / (t / a));
	} else if (z <= -3.4e+33) {
		tmp = x + (a * (y / z));
	} else if (z <= 2.25e+104) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+100:
		tmp = x - a
	elif z <= -2.9e+57:
		tmp = x + ((z - y) / (t / a))
	elif z <= -3.4e+33:
		tmp = x + (a * (y / z))
	elif z <= 2.25e+104:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+100)
		tmp = Float64(x - a);
	elseif (z <= -2.9e+57)
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	elseif (z <= -3.4e+33)
		tmp = Float64(x + Float64(a * Float64(y / z)));
	elseif (z <= 2.25e+104)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+100)
		tmp = x - a;
	elseif (z <= -2.9e+57)
		tmp = x + ((z - y) / (t / a));
	elseif (z <= -3.4e+33)
		tmp = x + (a * (y / z));
	elseif (z <= 2.25e+104)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+100], N[(x - a), $MachinePrecision], If[LessEqual[z, -2.9e+57], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.4e+33], N[(x + N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e+104], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.45e100 or 2.2499999999999999e104 < 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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 87.6%

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

   if -1.45e100 < z < -2.9000000000000002e57

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 77.0%

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

   if -2.9000000000000002e57 < z < -3.3999999999999999e33

   1. Initial program 99.7%

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

      1. associate-/r/ 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 70.0%

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

   6. Taylor expanded in z around inf 70.4%

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

      1. associate-*r/ 70.4%

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

      2. *-commutative 70.4%

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

      3. neg-mul-1 70.4%

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

      4. distribute-lft-neg-in 70.4%

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

      5. neg-mul-1 70.4%

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

      6. *-rgt-identity 70.4%

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

      7. times-frac 70.4%

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

      8. neg-mul-1 70.4%

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

      9. /-rgt-identity 70.4%

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

   8. Simplified 70.4%

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

   if -3.3999999999999999e33 < z < 2.2499999999999999e104

   1. Initial program 97.3%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 86.4%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+100}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+57}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+33}:\\ \;\;\;\;x + a \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+104}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + \left(-1 - t\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+46} \lor \neg \left(y \leq 7.5 \cdot 10^{+26}\right):\\ \;\;\;\;x + a \cdot \frac{y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ z (- -1.0 t))))
   (if (or (<= y -1.5e+46) (not (<= y 7.5e+26)))
     (+ x (* a (/ y t_1)))
     (- x (* a (/ z t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z + (-1.0 - t);
	double tmp;
	if ((y <= -1.5e+46) || !(y <= 7.5e+26)) {
		tmp = x + (a * (y / t_1));
	} else {
		tmp = x - (a * (z / t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + ((-1.0d0) - t)
    if ((y <= (-1.5d+46)) .or. (.not. (y <= 7.5d+26))) then
        tmp = x + (a * (y / t_1))
    else
        tmp = x - (a * (z / t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z + (-1.0 - t);
	double tmp;
	if ((y <= -1.5e+46) || !(y <= 7.5e+26)) {
		tmp = x + (a * (y / t_1));
	} else {
		tmp = x - (a * (z / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z + (-1.0 - t)
	tmp = 0
	if (y <= -1.5e+46) or not (y <= 7.5e+26):
		tmp = x + (a * (y / t_1))
	else:
		tmp = x - (a * (z / t_1))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z + Float64(-1.0 - t))
	tmp = 0.0
	if ((y <= -1.5e+46) || !(y <= 7.5e+26))
		tmp = Float64(x + Float64(a * Float64(y / t_1)));
	else
		tmp = Float64(x - Float64(a * Float64(z / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z + (-1.0 - t);
	tmp = 0.0;
	if ((y <= -1.5e+46) || ~((y <= 7.5e+26)))
		tmp = x + (a * (y / t_1));
	else
		tmp = x - (a * (z / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -1.5e+46], N[Not[LessEqual[y, 7.5e+26]], $MachinePrecision]], N[(x + N[(a * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000012e46 or 7.49999999999999941e26 < y

   1. Initial program 95.2%

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

   5. Taylor expanded in y around inf 87.8%

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

   if -1.50000000000000012e46 < y < 7.49999999999999941e26

   1. Initial program 97.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 92.6%

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

      1. mul-1-neg 92.6%

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

      2. associate--l+ 92.6%

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

      3. +-commutative 92.6%

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

      4. distribute-neg-frac2 92.6%

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

      5. +-commutative 92.6%

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

      6. distribute-neg-in 92.6%

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

      7. metadata-eval 92.6%

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

      8. unsub-neg 92.6%

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

      9. associate--r- 92.6%

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

   7. Simplified 92.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+46} \lor \neg \left(y \leq 7.5 \cdot 10^{+26}\right):\\ \;\;\;\;x + a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{z + \left(-1 - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+24}:\\ \;\;\;\;x - \frac{a}{\frac{z}{z - y}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+104}:\\ \;\;\;\;x + a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.9e+24)
   (- x (/ a (/ z (- z y))))
   (if (<= z 2e+104)
     (+ x (* a (/ y (+ z (- -1.0 t)))))
     (- x (* a (/ (- z y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.9e+24) {
		tmp = x - (a / (z / (z - y)));
	} else if (z <= 2e+104) {
		tmp = x + (a * (y / (z + (-1.0 - t))));
	} else {
		tmp = x - (a * ((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 (z <= (-3.9d+24)) then
        tmp = x - (a / (z / (z - y)))
    else if (z <= 2d+104) then
        tmp = x + (a * (y / (z + ((-1.0d0) - t))))
    else
        tmp = x - (a * ((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 (z <= -3.9e+24) {
		tmp = x - (a / (z / (z - y)));
	} else if (z <= 2e+104) {
		tmp = x + (a * (y / (z + (-1.0 - t))));
	} else {
		tmp = x - (a * ((z - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.9e+24:
		tmp = x - (a / (z / (z - y)))
	elif z <= 2e+104:
		tmp = x + (a * (y / (z + (-1.0 - t))))
	else:
		tmp = x - (a * ((z - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.9e+24)
		tmp = Float64(x - Float64(a / Float64(z / Float64(z - y))));
	elseif (z <= 2e+104)
		tmp = Float64(x + Float64(a * Float64(y / Float64(z + Float64(-1.0 - t)))));
	else
		tmp = Float64(x - Float64(a * Float64(Float64(z - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.9e+24)
		tmp = x - (a / (z / (z - y)));
	elseif (z <= 2e+104)
		tmp = x + (a * (y / (z + (-1.0 - t))));
	else
		tmp = x - (a * ((z - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.9e+24], N[(x - N[(a / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+104], N[(x + N[(a * N[(y / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8999999999999998e24

   1. Initial program 93.7%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 84.6%

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

      1. mul-1-neg 84.6%

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

   9. Simplified 84.6%

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

   if -3.8999999999999998e24 < z < 2e104

   1. Initial program 97.3%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 90.1%

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

   if 2e104 < z

   1. Initial program 99.9%

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

   5. Taylor expanded in z around inf 97.9%

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

      1. mul-1-neg 97.9%

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

   7. Simplified 97.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+24}:\\ \;\;\;\;x - \frac{a}{\frac{z}{z - y}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+104}:\\ \;\;\;\;x + a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+93} \lor \neg \left(z \leq 1.04 \cdot 10^{+108}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.5e+93) (not (<= z 1.04e+108)))
   (- x a)
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.5e+93) || !(z <= 1.04e+108)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - 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 ((z <= (-5.5d+93)) .or. (.not. (z <= 1.04d+108))) then
        tmp = x - a
    else
        tmp = x + (a * (y / ((-1.0d0) - 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 ((z <= -5.5e+93) || !(z <= 1.04e+108)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.5e+93) or not (z <= 1.04e+108):
		tmp = x - a
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.5e+93) || !(z <= 1.04e+108))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.5e+93) || ~((z <= 1.04e+108)))
		tmp = x - a;
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.5e+93], N[Not[LessEqual[z, 1.04e+108]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000003e93 or 1.04e108 < z

   1. Initial program 94.9%

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

   5. Taylor expanded in z around inf 85.8%

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

   if -5.5000000000000003e93 < z < 1.04e108

   1. Initial program 97.6%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 82.9%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+93} \lor \neg \left(z \leq 1.04 \cdot 10^{+108}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+22} \lor \neg \left(z \leq 2.5 \cdot 10^{+104}\right):\\ \;\;\;\;x - a \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8e+22) (not (<= z 2.5e+104)))
   (- x (* a (/ (- z y) z)))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8e+22) || !(z <= 2.5e+104)) {
		tmp = x - (a * ((z - y) / z));
	} else {
		tmp = x + (a * (y / (-1.0 - 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 ((z <= (-8d+22)) .or. (.not. (z <= 2.5d+104))) then
        tmp = x - (a * ((z - y) / z))
    else
        tmp = x + (a * (y / ((-1.0d0) - 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 ((z <= -8e+22) || !(z <= 2.5e+104)) {
		tmp = x - (a * ((z - y) / z));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8e+22) or not (z <= 2.5e+104):
		tmp = x - (a * ((z - y) / z))
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8e+22) || !(z <= 2.5e+104))
		tmp = Float64(x - Float64(a * Float64(Float64(z - y) / z)));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8e+22) || ~((z <= 2.5e+104)))
		tmp = x - (a * ((z - y) / z));
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8e+22], N[Not[LessEqual[z, 2.5e+104]], $MachinePrecision]], N[(x - N[(a * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8e22 or 2.4999999999999998e104 < 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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 89.4%

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

      1. mul-1-neg 89.4%

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

   7. Simplified 89.4%

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

   if -8e22 < z < 2.4999999999999998e104

   1. Initial program 97.3%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 87.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+22} \lor \neg \left(z \leq 2.5 \cdot 10^{+104}\right):\\ \;\;\;\;x - a \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+30}:\\ \;\;\;\;x - \frac{a}{\frac{z}{z - y}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+104}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+30)
   (- x (/ a (/ z (- z y))))
   (if (<= z 2e+104) (+ x (* a (/ y (- -1.0 t)))) (- x (* a (/ (- z y) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+30) {
		tmp = x - (a / (z / (z - y)));
	} else if (z <= 2e+104) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x - (a * ((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 (z <= (-2.5d+30)) then
        tmp = x - (a / (z / (z - y)))
    else if (z <= 2d+104) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x - (a * ((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 (z <= -2.5e+30) {
		tmp = x - (a / (z / (z - y)));
	} else if (z <= 2e+104) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x - (a * ((z - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+30:
		tmp = x - (a / (z / (z - y)))
	elif z <= 2e+104:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x - (a * ((z - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+30)
		tmp = Float64(x - Float64(a / Float64(z / Float64(z - y))));
	elseif (z <= 2e+104)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x - Float64(a * Float64(Float64(z - y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e+30)
		tmp = x - (a / (z / (z - y)));
	elseif (z <= 2e+104)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x - (a * ((z - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+30], N[(x - N[(a / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+104], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4999999999999999e30

   1. Initial program 93.7%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 84.6%

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

      1. mul-1-neg 84.6%

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

   9. Simplified 84.6%

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

   if -2.4999999999999999e30 < z < 2e104

   1. Initial program 97.3%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 87.0%

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

   if 2e104 < z

   1. Initial program 99.9%

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

   5. Taylor expanded in z around inf 97.9%

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

      1. mul-1-neg 97.9%

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

   7. Simplified 97.9%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+30}:\\ \;\;\;\;x - \frac{a}{\frac{z}{z - y}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+104}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+26} \lor \neg \left(z \leq 2.5 \cdot 10^{+104}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.25e+26) (not (<= z 2.5e+104))) (- x a) (- x (* a (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.25e+26) || !(z <= 2.5e+104)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (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 ((z <= (-2.25d+26)) .or. (.not. (z <= 2.5d+104))) then
        tmp = x - a
    else
        tmp = x - (a * (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 ((z <= -2.25e+26) || !(z <= 2.5e+104)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.25e+26) or not (z <= 2.5e+104):
		tmp = x - a
	else:
		tmp = x - (a * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.25e+26) || !(z <= 2.5e+104))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.25e+26) || ~((z <= 2.5e+104)))
		tmp = x - a;
	else
		tmp = x - (a * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.25e+26], N[Not[LessEqual[z, 2.5e+104]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.24999999999999989e26 or 2.4999999999999998e104 < 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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.6%

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

   if -2.24999999999999989e26 < z < 2.4999999999999998e104

   1. Initial program 97.3%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 90.1%

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

   6. Taylor expanded in t around inf 78.4%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+26} \lor \neg \left(z \leq 2.5 \cdot 10^{+104}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+33} \lor \neg \left(z \leq 5.1 \cdot 10^{+104}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.15e+33) (not (<= z 5.1e+104))) (- x a) (- x (/ a (/ t y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.15e+33) || !(z <= 5.1e+104)) {
		tmp = x - a;
	} else {
		tmp = x - (a / (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.15d+33)) .or. (.not. (z <= 5.1d+104))) then
        tmp = x - a
    else
        tmp = x - (a / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.15e+33) || !(z <= 5.1e+104)) {
		tmp = x - a;
	} else {
		tmp = x - (a / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.15e+33) or not (z <= 5.1e+104):
		tmp = x - a
	else:
		tmp = x - (a / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.15e+33) || !(z <= 5.1e+104))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.15e+33) || ~((z <= 5.1e+104)))
		tmp = x - a;
	else
		tmp = x - (a / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.15e+33], N[Not[LessEqual[z, 5.1e+104]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15000000000000014e33 or 5.1000000000000002e104 < 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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.6%

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

   if -2.15000000000000014e33 < z < 5.1000000000000002e104

   1. Initial program 97.3%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 90.1%

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

   6. Taylor expanded in t around inf 78.4%

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

      1. *-commutative 78.4%

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

      2. clear-num 78.4%

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

      3. un-div-inv 78.4%

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

   8. Applied egg-rr 78.4%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+33} \lor \neg \left(z \leq 5.1 \cdot 10^{+104}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 72.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+14} \lor \neg \left(z \leq 1.62 \cdot 10^{+97}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e+14) (not (<= z 1.62e+97))) (- x a) (- x (* a y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+14) || !(z <= 1.62e+97)) {
		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 <= (-4.5d+14)) .or. (.not. (z <= 1.62d+97))) 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 <= -4.5e+14) || !(z <= 1.62e+97)) {
		tmp = x - a;
	} else {
		tmp = x - (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e+14) or not (z <= 1.62e+97):
		tmp = x - a
	else:
		tmp = x - (a * y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e+14) || !(z <= 1.62e+97))
		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 <= -4.5e+14) || ~((z <= 1.62e+97)))
		tmp = x - a;
	else
		tmp = x - (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e+14], N[Not[LessEqual[z, 1.62e+97]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e14 or 1.62e97 < z

   1. Initial program 96.0%

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

   5. Taylor expanded in z around inf 78.1%

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

   if -4.5e14 < z < 1.62e97

   1. Initial program 97.2%

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

   3. Taylor expanded in t around 0 67.7%

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

   4. Taylor expanded in z around 0 65.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+14} \lor \neg \left(z \leq 1.62 \cdot 10^{+97}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+16} \lor \neg \left(z \leq 2 \cdot 10^{+104}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e+16) (not (<= z 2e+104))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+16) || !(z <= 2e+104)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.2d+16)) .or. (.not. (z <= 2d+104))) then
        tmp = x - a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+16) || !(z <= 2e+104)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e+16) or not (z <= 2e+104):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e+16) || !(z <= 2e+104))
		tmp = Float64(x - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.2e+16) || ~((z <= 2e+104)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e+16], N[Not[LessEqual[z, 2e+104]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e16 or 2e104 < 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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.0%

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

   if -1.2e16 < z < 2e104

   1. Initial program 97.3%

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

   3. Taylor expanded in t around inf 78.9%

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

   4. Taylor expanded in x around inf 57.1%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+16} \lor \neg \left(z \leq 2 \cdot 10^{+104}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (a / (1.0d0 - (z - t))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

   1. clear-num 96.7%

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

   2. associate-/r/ 96.7%

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

   3. clear-num 97.7%

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

4. Applied egg-rr 97.7%

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

5. Final simplification 97.7%

   \[\leadsto x - \left(y - z\right) \cdot \frac{a}{1 - \left(z - t\right)} \]
6. Add Preprocessing

Alternative 16: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 * ((y - z) / (1.0d0 - (z - t))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

   1. associate-/r/ 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

   \[\leadsto x - a \cdot \frac{y - z}{1 - \left(z - t\right)} \]
6. Add Preprocessing

Alternative 17: 55.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+162} \lor \neg \left(a \leq 2.7 \cdot 10^{+143}\right):\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.3e+162) (not (<= a 2.7e+143))) (- a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.3e+162) || !(a <= 2.7e+143)) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.3d+162)) .or. (.not. (a <= 2.7d+143))) then
        tmp = -a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.3e+162) || !(a <= 2.7e+143)) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.3e+162) or not (a <= 2.7e+143):
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.3e+162) || !(a <= 2.7e+143))
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.3e+162) || ~((a <= 2.7e+143)))
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.3e+162], N[Not[LessEqual[a, 2.7e+143]], $MachinePrecision]], (-a), x]

Derivation

1. Split input into 2 regimes

2. if a < -1.3e162 or 2.7000000000000002e143 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 70.0%

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

   4. Taylor expanded in x around 0 28.1%

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

      1. mul-1-neg 28.1%

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

      2. associate-*r/ 60.1%

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

      3. distribute-rgt-neg-in 60.1%

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

      4. distribute-neg-frac2 60.1%

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

   6. Simplified 60.1%

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

   7. Taylor expanded in z around inf 32.2%

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

      1. mul-1-neg 32.2%

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

   9. Simplified 32.2%

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

   if -1.3e162 < a < 2.7000000000000002e143

   1. Initial program 95.5%

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

   3. Taylor expanded in t around inf 63.8%

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

   4. Taylor expanded in x around inf 67.5%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+162} \lor \neg \left(a \leq 2.7 \cdot 10^{+143}\right):\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 53.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

3. Taylor expanded in t around inf 60.7%

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

4. Taylor expanded in x around inf 53.2%

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

5. Final simplification 53.2%

   \[\leadsto x \]
6. Add Preprocessing

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 2024055 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))