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

Percentage Accurate: 97.3% → 99.6%

Time: 12.1s

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: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

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

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 97.2%

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

   1. associate-/r/ 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 2: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -38000000000 \lor \neg \left(z \leq 25000\right):\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y + \left(-1 - t\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -38000000000.0) (not (<= z 25000.0)))
   (+ x (* a (+ -1.0 (/ (+ y (- -1.0 t)) z))))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -38000000000.0) || !(z <= 25000.0)) {
		tmp = x + (a * (-1.0 + ((y + (-1.0 - t)) / 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 <= (-38000000000.0d0)) .or. (.not. (z <= 25000.0d0))) then
        tmp = x + (a * ((-1.0d0) + ((y + ((-1.0d0) - t)) / 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 <= -38000000000.0) || !(z <= 25000.0)) {
		tmp = x + (a * (-1.0 + ((y + (-1.0 - t)) / z)));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -38000000000.0) or not (z <= 25000.0):
		tmp = x + (a * (-1.0 + ((y + (-1.0 - t)) / z)))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -38000000000.0) || !(z <= 25000.0))
		tmp = Float64(x + Float64(a * Float64(-1.0 + Float64(Float64(y + Float64(-1.0 - t)) / 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 <= -38000000000.0) || ~((z <= 25000.0)))
		tmp = x + (a * (-1.0 + ((y + (-1.0 - t)) / z)));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -38000000000.0], N[Not[LessEqual[z, 25000.0]], $MachinePrecision]], N[(x + N[(a * N[(-1.0 + N[(N[(y + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $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 < -3.8e10 or 25000 < z

   1. Initial program 95.5%

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

      1. associate-/r/ 99.9%

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

   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 80.3%

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

      1. associate--l+ 80.3%

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

      2. associate-*r/ 80.3%

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

      3. associate-*r/ 80.3%

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

      4. mul-1-neg 80.3%

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

      5. div-sub 80.3%

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

      6. mul-1-neg 80.3%

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

      7. distribute-lft-out-- 80.3%

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

      8. associate-*r/ 80.3%

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

      9. mul-1-neg 80.3%

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

      10. unsub-neg 80.3%

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

      11. sub-neg 80.3%

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

      12. mul-1-neg 80.3%

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

      13. distribute-lft-in 80.3%

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

      14. metadata-eval 80.3%

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

      15. mul-1-neg 80.3%

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

      16. unsub-neg 80.3%

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

   7. Simplified 80.3%

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

   if -3.8e10 < z < 25000

   1. Initial program 99.0%

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

      1. associate-/r/ 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around 0 94.2%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -38000000000 \lor \neg \left(z \leq 25000\right):\\ \;\;\;\;x + a \cdot \left(-1 + \frac{y + \left(-1 - t\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+75}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-29}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+75)
   (- x a)
   (if (<= z -3.9e+28)
     (+ x (/ z (/ t a)))
     (if (<= z 8e-29) (- x (* y a)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+75) {
		tmp = x - a;
	} else if (z <= -3.9e+28) {
		tmp = x + (z / (t / a));
	} else if (z <= 8e-29) {
		tmp = x - (y * a);
	} 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+75)) then
        tmp = x - a
    else if (z <= (-3.9d+28)) then
        tmp = x + (z / (t / a))
    else if (z <= 8d-29) then
        tmp = x - (y * a)
    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+75) {
		tmp = x - a;
	} else if (z <= -3.9e+28) {
		tmp = x + (z / (t / a));
	} else if (z <= 8e-29) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+75:
		tmp = x - a
	elif z <= -3.9e+28:
		tmp = x + (z / (t / a))
	elif z <= 8e-29:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+75)
		tmp = Float64(x - a);
	elseif (z <= -3.9e+28)
		tmp = Float64(x + Float64(z / Float64(t / a)));
	elseif (z <= 8e-29)
		tmp = Float64(x - Float64(y * a));
	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+75)
		tmp = x - a;
	elseif (z <= -3.9e+28)
		tmp = x + (z / (t / a));
	elseif (z <= 8e-29)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+75], N[(x - a), $MachinePrecision], If[LessEqual[z, -3.9e+28], N[(x + N[(z / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-29], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04999999999999999e75 or 7.99999999999999955e-29 < z

   1. Initial program 95.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 71.6%

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

   if -1.04999999999999999e75 < z < -3.8999999999999999e28

   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 inf 74.6%

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

   4. Taylor expanded in y around 0 74.8%

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

      1. neg-mul-1 74.8%

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

   6. Simplified 74.8%

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

   if -3.8999999999999999e28 < z < 7.99999999999999955e-29

   1. Initial program 99.0%

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

      1. associate-/r/ 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around 0 93.3%

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

   6. Taylor expanded in t around 0 70.9%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+75}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-29}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -530000000 \lor \neg \left(z \leq 2.55 \cdot 10^{-5}\right):\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -530000000.0) (not (<= z 2.55e-5)))
   (- 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 <= -530000000.0) || !(z <= 2.55e-5)) {
		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 <= (-530000000.0d0)) .or. (.not. (z <= 2.55d-5))) 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 <= -530000000.0) || !(z <= 2.55e-5)) {
		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 <= -530000000.0) or not (z <= 2.55e-5):
		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 <= -530000000.0) || !(z <= 2.55e-5))
		tmp = Float64(x - Float64(Float64(z - y) / 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 <= -530000000.0) || ~((z <= 2.55e-5)))
		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, -530000000.0], N[Not[LessEqual[z, 2.55e-5]], $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 < -5.3e8 or 2.54999999999999998e-5 < z

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf 77.7%

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

      1. associate-*r/ 77.7%

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

      2. neg-mul-1 77.7%

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

   5. Simplified 77.7%

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

   if -5.3e8 < z < 2.54999999999999998e-5

   1. Initial program 99.0%

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

      1. associate-/r/ 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around 0 94.2%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -530000000 \lor \neg \left(z \leq 2.55 \cdot 10^{-5}\right):\\ \;\;\;\;x - \frac{z - y}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+76} \lor \neg \left(z \leq 1.2 \cdot 10^{+64}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.55e+76) (not (<= z 1.2e+64)))
   (- x a)
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.55e+76) || !(z <= 1.2e+64)) {
		tmp = x - 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 <= (-2.55d+76)) .or. (.not. (z <= 1.2d+64))) then
        tmp = x - 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 <= -2.55e+76) || !(z <= 1.2e+64)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.55e+76) or not (z <= 1.2e+64):
		tmp = x - a
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.55e+76) || !(z <= 1.2e+64))
		tmp = Float64(x - 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 <= -2.55e+76) || ~((z <= 1.2e+64)))
		tmp = x - 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, -2.55e+76], N[Not[LessEqual[z, 1.2e+64]], $MachinePrecision]], N[(x - a), $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 < -2.5500000000000001e76 or 1.2e64 < z

   1. Initial program 94.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 73.9%

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

   if -2.5500000000000001e76 < z < 1.2e64

   1. Initial program 99.2%

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

      1. associate-/r/ 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around 0 85.2%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+76} \lor \neg \left(z \leq 1.2 \cdot 10^{+64}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+148} \lor \neg \left(t \leq 7.8 \cdot 10^{+163}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.9e+148) (not (<= t 7.8e+163)))
   (+ x (/ z (/ t a)))
   (+ x (* a (/ y (+ z -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.9e+148) || !(t <= 7.8e+163)) {
		tmp = x + (z / (t / a));
	} else {
		tmp = x + (a * (y / (z + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.9d+148)) .or. (.not. (t <= 7.8d+163))) then
        tmp = x + (z / (t / a))
    else
        tmp = x + (a * (y / (z + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.9e+148) || !(t <= 7.8e+163)) {
		tmp = x + (z / (t / a));
	} else {
		tmp = x + (a * (y / (z + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.9e+148) or not (t <= 7.8e+163):
		tmp = x + (z / (t / a))
	else:
		tmp = x + (a * (y / (z + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.9e+148) || !(t <= 7.8e+163))
		tmp = Float64(x + Float64(z / Float64(t / a)));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(z + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.9e+148) || ~((t <= 7.8e+163)))
		tmp = x + (z / (t / a));
	else
		tmp = x + (a * (y / (z + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.9e+148], N[Not[LessEqual[t, 7.8e+163]], $MachinePrecision]], N[(x + N[(z / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.90000000000000002e148 or 7.80000000000000047e163 < t

   1. Initial program 97.0%

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

   3. Taylor expanded in t around inf 94.1%

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

   4. Taylor expanded in y around 0 79.6%

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

      1. neg-mul-1 79.6%

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

   6. Simplified 79.6%

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

   if -3.90000000000000002e148 < t < 7.80000000000000047e163

   1. Initial program 97.2%

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

      1. associate-/r/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t around 0 76.5%

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

   6. Taylor expanded in y around inf 66.5%

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

      1. associate-/l* 68.8%

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

   8. Simplified 68.8%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+148} \lor \neg \left(t \leq 7.8 \cdot 10^{+163}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+17} \lor \neg \left(z \leq 8 \cdot 10^{-29}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.05e+17) (not (<= z 8e-29))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.05e+17) || !(z <= 8e-29)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.05d+17)) .or. (.not. (z <= 8d-29))) then
        tmp = x - a
    else
        tmp = x - (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.05e+17) || !(z <= 8e-29)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.05e+17) or not (z <= 8e-29):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.05e+17) || !(z <= 8e-29))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.05e+17) || ~((z <= 8e-29)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.05e+17], N[Not[LessEqual[z, 8e-29]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e17 or 7.99999999999999955e-29 < z

   1. Initial program 95.6%

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

      1. associate-/r/ 99.9%

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

   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 68.3%

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

   if -1.05e17 < z < 7.99999999999999955e-29

   1. Initial program 99.0%

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

      1. associate-/r/ 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in z around 0 94.1%

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

   6. Taylor expanded in t around 0 71.3%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+17} \lor \neg \left(z \leq 8 \cdot 10^{-29}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+222}:\\ \;\;\;\;a \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+186}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.5e+222) (* a (/ z t)) (if (<= t 4.6e+186) (- x a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e+222) {
		tmp = a * (z / t);
	} else if (t <= 4.6e+186) {
		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 (t <= (-5.5d+222)) then
        tmp = a * (z / t)
    else if (t <= 4.6d+186) 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 (t <= -5.5e+222) {
		tmp = a * (z / t);
	} else if (t <= 4.6e+186) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.5e+222:
		tmp = a * (z / t)
	elif t <= 4.6e+186:
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.5e+222)
		tmp = Float64(a * Float64(z / t));
	elseif (t <= 4.6e+186)
		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 (t <= -5.5e+222)
		tmp = a * (z / t);
	elseif (t <= 4.6e+186)
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.5e+222], N[(a * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+186], N[(x - a), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if t < -5.4999999999999999e222

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-/r/ 96.2%

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

      4. distribute-rgt-neg-in 96.2%

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

      5. associate-*l/ 80.5%

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

      6. associate-/l* 99.7%

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

      7. fma-define 99.8%

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

      8. distribute-frac-neg 99.8%

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

      9. distribute-neg-frac2 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. sub-neg 99.8%

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

      12. distribute-neg-in 99.8%

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

      13. remove-double-neg 99.8%

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

      14. +-commutative 99.8%

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

      15. sub-neg 99.8%

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

      16. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around -inf 45.1%

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

   6. Taylor expanded in t around inf 44.9%

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

      1. mul-1-neg 44.9%

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

      2. associate-/l* 56.6%

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

      3. distribute-rgt-neg-in 56.6%

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

   8. Simplified 56.6%

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

   9. Taylor expanded in y around 0 37.3%

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

       1. associate-/l* 45.1%

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

   11. Simplified 45.1%

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

   if -5.4999999999999999e222 < t < 4.60000000000000027e186

   1. Initial program 97.0%

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

      1. associate-/r/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 64.0%

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

   if 4.60000000000000027e186 < t

   1. Initial program 95.2%

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

      1. sub-neg 95.2%

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

      2. +-commutative 95.2%

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

      3. associate-/r/ 95.2%

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

      4. distribute-rgt-neg-in 95.2%

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

      5. associate-*l/ 86.0%

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

      6. associate-/l* 95.2%

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

      7. fma-define 95.2%

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

      8. distribute-frac-neg 95.2%

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

      9. distribute-neg-frac2 95.2%

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

      10. distribute-neg-in 95.2%

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

      11. sub-neg 95.2%

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

      12. distribute-neg-in 95.2%

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

      13. remove-double-neg 95.2%

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

      14. +-commutative 95.2%

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

      15. sub-neg 95.2%

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

      16. metadata-eval 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in a around 0 76.1%

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

Alternative 9: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+210}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+188}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e+210) x (if (<= t 4.6e+188) (- x a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+210) {
		tmp = x;
	} else if (t <= 4.6e+188) {
		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 (t <= (-4.2d+210)) then
        tmp = x
    else if (t <= 4.6d+188) 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 (t <= -4.2e+210) {
		tmp = x;
	} else if (t <= 4.6e+188) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.2e+210:
		tmp = x
	elif t <= 4.6e+188:
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e+210)
		tmp = x;
	elseif (t <= 4.6e+188)
		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 (t <= -4.2e+210)
		tmp = x;
	elseif (t <= 4.6e+188)
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e+210], x, If[LessEqual[t, 4.6e+188], N[(x - a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -4.1999999999999997e210 or 4.60000000000000023e188 < t

   1. Initial program 98.0%

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

      1. sub-neg 98.0%

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

      2. +-commutative 98.0%

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

      3. associate-/r/ 96.0%

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

      4. distribute-rgt-neg-in 96.0%

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

      5. associate-*l/ 82.1%

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

      6. associate-/l* 97.8%

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

      7. fma-define 97.9%

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

      8. distribute-frac-neg 97.9%

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

      9. distribute-neg-frac2 97.9%

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

      10. distribute-neg-in 97.9%

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

      11. sub-neg 97.9%

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

      12. distribute-neg-in 97.9%

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

      13. remove-double-neg 97.9%

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

      14. +-commutative 97.9%

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

      15. sub-neg 97.9%

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

      16. metadata-eval 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in a around 0 58.0%

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

   if -4.1999999999999997e210 < t < 4.60000000000000023e188

   1. Initial program 97.0%

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

      1. associate-/r/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 64.0%

      \[\leadsto x - \color{blue}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 54.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+142} \lor \neg \left(a \leq 4.8 \cdot 10^{+121}\right):\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3e+142) (not (<= a 4.8e+121))) (- a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3e+142) || !(a <= 4.8e+121)) {
		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 <= (-3d+142)) .or. (.not. (a <= 4.8d+121))) 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 <= -3e+142) || !(a <= 4.8e+121)) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3e+142) or not (a <= 4.8e+121):
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3e+142) || !(a <= 4.8e+121))
		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 <= -3e+142) || ~((a <= 4.8e+121)))
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3e+142], N[Not[LessEqual[a, 4.8e+121]], $MachinePrecision]], (-a), x]

Derivation

1. Split input into 2 regimes

2. if a < -2.99999999999999975e142 or 4.8e121 < a

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-/r/ 96.1%

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

      4. distribute-rgt-neg-in 96.1%

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

      5. associate-*l/ 52.3%

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

      6. associate-/l* 99.8%

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

      7. fma-define 99.8%

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

      8. distribute-frac-neg 99.8%

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

      9. distribute-neg-frac2 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. sub-neg 99.8%

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

      12. distribute-neg-in 99.8%

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

      13. remove-double-neg 99.8%

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

      14. +-commutative 99.8%

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

      15. sub-neg 99.8%

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

      16. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around -inf 44.1%

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

   6. Taylor expanded in z around inf 32.6%

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

      1. neg-mul-1 32.6%

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

   8. Simplified 32.6%

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

   if -2.99999999999999975e142 < a < 4.8e121

   1. Initial program 96.0%

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

      1. sub-neg 96.0%

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

      2. +-commutative 96.0%

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

      3. associate-/r/ 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. associate-*l/ 95.6%

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

      6. associate-/l* 97.0%

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

      7. fma-define 97.0%

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

      8. distribute-frac-neg 97.0%

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

      9. distribute-neg-frac2 97.0%

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

      10. distribute-neg-in 97.0%

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

      11. sub-neg 97.0%

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

      12. distribute-neg-in 97.0%

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

      13. remove-double-neg 97.0%

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

      14. +-commutative 97.0%

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

      15. sub-neg 97.0%

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

      16. metadata-eval 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in a around 0 65.0%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+142} \lor \neg \left(a \leq 4.8 \cdot 10^{+121}\right):\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.6% 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 97.2%

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

   1. sub-neg 97.2%

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

   2. +-commutative 97.2%

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

   3. associate-/r/ 98.8%

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

   4. distribute-rgt-neg-in 98.8%

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

   5. associate-*l/ 82.7%

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

   6. associate-/l* 97.8%

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

   7. fma-define 97.8%

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

   8. distribute-frac-neg 97.8%

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

   9. distribute-neg-frac2 97.8%

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

   10. distribute-neg-in 97.8%

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

   11. sub-neg 97.8%

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

   12. distribute-neg-in 97.8%

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

   13. remove-double-neg 97.8%

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

   14. +-commutative 97.8%

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

   15. sub-neg 97.8%

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

   16. metadata-eval 97.8%

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

3. Simplified 97.8%

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

5. Taylor expanded in a around 0 49.6%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Alternative 12: 3.2% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. sub-neg 97.2%

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

   2. +-commutative 97.2%

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

   3. associate-/r/ 98.8%

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

   4. distribute-rgt-neg-in 98.8%

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

   5. associate-*l/ 82.7%

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

   6. associate-/l* 97.8%

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

   7. fma-define 97.8%

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

   8. distribute-frac-neg 97.8%

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

   9. distribute-neg-frac2 97.8%

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

   10. distribute-neg-in 97.8%

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

   11. sub-neg 97.8%

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

   12. distribute-neg-in 97.8%

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

   13. remove-double-neg 97.8%

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

   14. +-commutative 97.8%

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

   15. sub-neg 97.8%

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

   16. metadata-eval 97.8%

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

3. Simplified 97.8%

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

5. Taylor expanded in a around -inf 37.3%

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

6. Taylor expanded in z around inf 18.0%

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

   1. neg-mul-1 18.0%

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

8. Simplified 18.0%

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

   1. neg-sub0 18.0%

      \[\leadsto \color{blue}{0 - a} \]

   2. sub-neg 18.0%

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

   3. add-sqr-sqrt 7.4%

      \[\leadsto 0 + \color{blue}{\sqrt{-a} \cdot \sqrt{-a}} \]

   4. sqrt-unprod 6.9%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}} \]

   5. sqr-neg 6.9%

      \[\leadsto 0 + \sqrt{\color{blue}{a \cdot a}} \]

   6. sqrt-unprod 1.7%

      \[\leadsto 0 + \color{blue}{\sqrt{a} \cdot \sqrt{a}} \]

   7. add-sqr-sqrt 3.4%

      \[\leadsto 0 + \color{blue}{a} \]

10. Applied egg-rr 3.4%

    \[\leadsto \color{blue}{0 + a} \]

11. Taylor expanded in a around 0 3.4%

    \[\leadsto \color{blue}{a} \]
12. Add Preprocessing

Developer Target 1: 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 2024172 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (/ (- y z) (+ (- t z) 1)) a)))

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