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

Percentage Accurate: 97.0% → 99.6%

Time: 14.2s

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: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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. Final simplification 99.9%

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

Alternative 2: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{t}{a}}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+142}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+61}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ t a)))))
   (if (<= z -4.8e+142)
     (- x a)
     (if (<= z -2.05e+82)
       t_1
       (if (<= z -2.5e+61)
         (- x a)
         (if (<= z 1.76e-90) x (if (<= z 2.25e+170) t_1 (- x a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (t / a));
	double tmp;
	if (z <= -4.8e+142) {
		tmp = x - a;
	} else if (z <= -2.05e+82) {
		tmp = t_1;
	} else if (z <= -2.5e+61) {
		tmp = x - a;
	} else if (z <= 1.76e-90) {
		tmp = x;
	} else if (z <= 2.25e+170) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / (t / a))
    if (z <= (-4.8d+142)) then
        tmp = x - a
    else if (z <= (-2.05d+82)) then
        tmp = t_1
    else if (z <= (-2.5d+61)) then
        tmp = x - a
    else if (z <= 1.76d-90) then
        tmp = x
    else if (z <= 2.25d+170) then
        tmp = t_1
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (t / a));
	double tmp;
	if (z <= -4.8e+142) {
		tmp = x - a;
	} else if (z <= -2.05e+82) {
		tmp = t_1;
	} else if (z <= -2.5e+61) {
		tmp = x - a;
	} else if (z <= 1.76e-90) {
		tmp = x;
	} else if (z <= 2.25e+170) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (t / a))
	tmp = 0
	if z <= -4.8e+142:
		tmp = x - a
	elif z <= -2.05e+82:
		tmp = t_1
	elif z <= -2.5e+61:
		tmp = x - a
	elif z <= 1.76e-90:
		tmp = x
	elif z <= 2.25e+170:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(t / a)))
	tmp = 0.0
	if (z <= -4.8e+142)
		tmp = Float64(x - a);
	elseif (z <= -2.05e+82)
		tmp = t_1;
	elseif (z <= -2.5e+61)
		tmp = Float64(x - a);
	elseif (z <= 1.76e-90)
		tmp = x;
	elseif (z <= 2.25e+170)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (t / a));
	tmp = 0.0;
	if (z <= -4.8e+142)
		tmp = x - a;
	elseif (z <= -2.05e+82)
		tmp = t_1;
	elseif (z <= -2.5e+61)
		tmp = x - a;
	elseif (z <= 1.76e-90)
		tmp = x;
	elseif (z <= 2.25e+170)
		tmp = t_1;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+142], N[(x - a), $MachinePrecision], If[LessEqual[z, -2.05e+82], t$95$1, If[LessEqual[z, -2.5e+61], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.76e-90], x, If[LessEqual[z, 2.25e+170], t$95$1, N[(x - a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7999999999999998e142 or -2.04999999999999998e82 < z < -2.50000000000000009e61 or 2.25000000000000011e170 < z

   1. Initial program 91.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 86.8%

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

   if -4.7999999999999998e142 < z < -2.04999999999999998e82 or 1.7600000000000001e-90 < z < 2.25000000000000011e170

   1. Initial program 99.8%

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

      1. associate-/r/ 99.8%

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

   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 t around inf 63.2%

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

      1. associate-/l* 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in y around 0 69.2%

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

      1. mul-1-neg 69.2%

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

   10. Simplified 69.2%

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

   11. Taylor expanded in x around 0 65.4%

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

       1. associate-/l* 69.2%

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

       2. associate-/r/ 70.6%

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

   13. Simplified 70.6%

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

       1. *-commutative 70.6%

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

       2. clear-num 72.2%

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

       3. div-inv 72.2%

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

   15. Applied egg-rr 72.2%

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

   if -2.50000000000000009e61 < z < 1.7600000000000001e-90

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 58.8%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+142}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+82}:\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+61}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+170}:\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{t}{a}}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+142}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{+59}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-89}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ t a)))))
   (if (<= z -4.8e+142)
     (- x a)
     (if (<= z -2.35e+82)
       t_1
       (if (<= z -1.42e+59)
         (- x a)
         (if (<= z 4e-89)
           (- x (* y (/ a t)))
           (if (<= z 2.25e+170) t_1 (- x a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (t / a));
	double tmp;
	if (z <= -4.8e+142) {
		tmp = x - a;
	} else if (z <= -2.35e+82) {
		tmp = t_1;
	} else if (z <= -1.42e+59) {
		tmp = x - a;
	} else if (z <= 4e-89) {
		tmp = x - (y * (a / t));
	} else if (z <= 2.25e+170) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / (t / a))
    if (z <= (-4.8d+142)) then
        tmp = x - a
    else if (z <= (-2.35d+82)) then
        tmp = t_1
    else if (z <= (-1.42d+59)) then
        tmp = x - a
    else if (z <= 4d-89) then
        tmp = x - (y * (a / t))
    else if (z <= 2.25d+170) then
        tmp = t_1
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z / (t / a));
	double tmp;
	if (z <= -4.8e+142) {
		tmp = x - a;
	} else if (z <= -2.35e+82) {
		tmp = t_1;
	} else if (z <= -1.42e+59) {
		tmp = x - a;
	} else if (z <= 4e-89) {
		tmp = x - (y * (a / t));
	} else if (z <= 2.25e+170) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z / (t / a))
	tmp = 0
	if z <= -4.8e+142:
		tmp = x - a
	elif z <= -2.35e+82:
		tmp = t_1
	elif z <= -1.42e+59:
		tmp = x - a
	elif z <= 4e-89:
		tmp = x - (y * (a / t))
	elif z <= 2.25e+170:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z / Float64(t / a)))
	tmp = 0.0
	if (z <= -4.8e+142)
		tmp = Float64(x - a);
	elseif (z <= -2.35e+82)
		tmp = t_1;
	elseif (z <= -1.42e+59)
		tmp = Float64(x - a);
	elseif (z <= 4e-89)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	elseif (z <= 2.25e+170)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z / (t / a));
	tmp = 0.0;
	if (z <= -4.8e+142)
		tmp = x - a;
	elseif (z <= -2.35e+82)
		tmp = t_1;
	elseif (z <= -1.42e+59)
		tmp = x - a;
	elseif (z <= 4e-89)
		tmp = x - (y * (a / t));
	elseif (z <= 2.25e+170)
		tmp = t_1;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+142], N[(x - a), $MachinePrecision], If[LessEqual[z, -2.35e+82], t$95$1, If[LessEqual[z, -1.42e+59], N[(x - a), $MachinePrecision], If[LessEqual[z, 4e-89], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e+170], t$95$1, N[(x - a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7999999999999998e142 or -2.35e82 < z < -1.42000000000000005e59 or 2.25000000000000011e170 < z

   1. Initial program 91.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 87.0%

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

   if -4.7999999999999998e142 < z < -2.35e82 or 4.00000000000000015e-89 < z < 2.25000000000000011e170

   1. Initial program 99.8%

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

      1. associate-/r/ 99.8%

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

   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 t around inf 62.6%

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

      1. associate-/l* 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in y around 0 70.2%

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

      1. mul-1-neg 70.2%

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

   10. Simplified 70.2%

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

   11. Taylor expanded in x around 0 66.3%

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

       1. associate-/l* 70.2%

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

       2. associate-/r/ 71.6%

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

   13. Simplified 71.6%

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

       1. *-commutative 71.6%

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

       2. clear-num 73.2%

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

       3. div-inv 73.2%

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

   15. Applied egg-rr 73.2%

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

   if -1.42000000000000005e59 < z < 4.00000000000000015e-89

   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 inf 64.5%

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

   4. Taylor expanded in y around inf 62.5%

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

      1. *-commutative 62.5%

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

      2. associate-*r/ 64.3%

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

   6. Simplified 64.3%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+142}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+82}:\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{+59}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-89}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+170}:\\ \;\;\;\;x + \frac{z}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+28} \lor \neg \left(z \leq 4.6 \cdot 10^{-45}\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.55e+28) (not (<= z 4.6e-45)))
   (+ x (* a (/ z (+ (- t z) 1.0))))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.55e+28) || !(z <= 4.6e-45)) {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	} 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 <= (-3.55d+28)) .or. (.not. (z <= 4.6d-45))) then
        tmp = x + (a * (z / ((t - z) + 1.0d0)))
    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 <= -3.55e+28) || !(z <= 4.6e-45)) {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.55e+28) or not (z <= 4.6e-45):
		tmp = x + (a * (z / ((t - z) + 1.0)))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.55e+28) || !(z <= 4.6e-45))
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(t - z) + 1.0))));
	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 <= -3.55e+28) || ~((z <= 4.6e-45)))
		tmp = x + (a * (z / ((t - z) + 1.0)));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.55e+28], N[Not[LessEqual[z, 4.6e-45]], $MachinePrecision]], N[(x + N[(a * N[(z / N[(N[(t - z), $MachinePrecision] + 1.0), $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 < -3.55e28 or 4.59999999999999983e-45 < z

   1. Initial program 94.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 69.8%

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

      1. mul-1-neg 69.8%

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

      2. *-commutative 69.8%

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

      3. associate--l+ 69.8%

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

      4. +-commutative 69.8%

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

      5. associate-*r/ 87.3%

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

      6. distribute-rgt-neg-in 87.3%

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

      7. distribute-neg-frac 87.3%

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

      8. +-commutative 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in x around 0 69.8%

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

      1. +-commutative 69.8%

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

      2. associate-/l* 90.6%

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

      3. sub-neg 90.6%

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

      4. associate-+r+ 90.6%

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

      5. mul-1-neg 90.6%

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

      6. +-commutative 90.6%

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

      7. mul-1-neg 90.6%

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

      8. sub-neg 90.6%

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

      9. associate--r- 90.6%

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

      10. sub-neg 90.6%

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

      11. metadata-eval 90.6%

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

   10. Simplified 90.6%

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

       1. div-inv 90.6%

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

       2. clear-num 90.6%

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

       3. associate--r+ 90.6%

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

       4. sub-neg 90.6%

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

       5. metadata-eval 90.6%

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

   12. Applied egg-rr 90.6%

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

   if -3.55e28 < z < 4.59999999999999983e-45

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 93.1%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+28} \lor \neg \left(z \leq 4.6 \cdot 10^{-45}\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+28} \lor \neg \left(z \leq 6.5 \cdot 10^{-45}\right):\\ \;\;\;\;x + \frac{a}{\frac{t + 1}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.55e+28) (not (<= z 6.5e-45)))
   (+ x (/ a (+ (/ (+ t 1.0) z) -1.0)))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.55e+28) || !(z <= 6.5e-45)) {
		tmp = x + (a / (((t + 1.0) / z) + -1.0));
	} 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 <= (-3.55d+28)) .or. (.not. (z <= 6.5d-45))) then
        tmp = x + (a / (((t + 1.0d0) / z) + (-1.0d0)))
    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 <= -3.55e+28) || !(z <= 6.5e-45)) {
		tmp = x + (a / (((t + 1.0) / z) + -1.0));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.55e+28) or not (z <= 6.5e-45):
		tmp = x + (a / (((t + 1.0) / z) + -1.0))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.55e+28) || !(z <= 6.5e-45))
		tmp = Float64(x + Float64(a / Float64(Float64(Float64(t + 1.0) / z) + -1.0)));
	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 <= -3.55e+28) || ~((z <= 6.5e-45)))
		tmp = x + (a / (((t + 1.0) / z) + -1.0));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.55e+28], N[Not[LessEqual[z, 6.5e-45]], $MachinePrecision]], N[(x + N[(a / N[(N[(N[(t + 1.0), $MachinePrecision] / z), $MachinePrecision] + -1.0), $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 < -3.55e28 or 6.4999999999999995e-45 < z

   1. Initial program 94.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 69.8%

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

      1. mul-1-neg 69.8%

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

      2. *-commutative 69.8%

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

      3. associate--l+ 69.8%

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

      4. +-commutative 69.8%

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

      5. associate-*r/ 87.3%

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

      6. distribute-rgt-neg-in 87.3%

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

      7. distribute-neg-frac 87.3%

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

      8. +-commutative 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in x around 0 69.8%

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

      1. +-commutative 69.8%

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

      2. associate-/l* 90.6%

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

      3. sub-neg 90.6%

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

      4. associate-+r+ 90.6%

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

      5. mul-1-neg 90.6%

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

      6. +-commutative 90.6%

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

      7. mul-1-neg 90.6%

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

      8. sub-neg 90.6%

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

      9. associate--r- 90.6%

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

      10. sub-neg 90.6%

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

      11. metadata-eval 90.6%

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

   10. Simplified 90.6%

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

   11. Taylor expanded in a around 0 69.8%

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

       1. associate-/l* 90.6%

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

       2. div-sub 90.6%

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

       3. *-inverses 90.6%

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

   13. Simplified 90.6%

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

   if -3.55e28 < z < 6.4999999999999995e-45

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 93.1%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+28} \lor \neg \left(z \leq 6.5 \cdot 10^{-45}\right):\\ \;\;\;\;x + \frac{a}{\frac{t + 1}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+28} \lor \neg \left(z \leq 35000\right):\\ \;\;\;\;x + \frac{a}{\frac{t + 1}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{t + 1}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.9e+28) (not (<= z 35000.0)))
   (+ x (/ a (+ (/ (+ t 1.0) z) -1.0)))
   (+ x (/ (- z y) (/ (+ t 1.0) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.9e+28) || !(z <= 35000.0)) {
		tmp = x + (a / (((t + 1.0) / z) + -1.0));
	} else {
		tmp = x + ((z - y) / ((t + 1.0) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.9d+28)) .or. (.not. (z <= 35000.0d0))) then
        tmp = x + (a / (((t + 1.0d0) / z) + (-1.0d0)))
    else
        tmp = x + ((z - y) / ((t + 1.0d0) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.9e+28) || !(z <= 35000.0)) {
		tmp = x + (a / (((t + 1.0) / z) + -1.0));
	} else {
		tmp = x + ((z - y) / ((t + 1.0) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.9e+28) or not (z <= 35000.0):
		tmp = x + (a / (((t + 1.0) / z) + -1.0))
	else:
		tmp = x + ((z - y) / ((t + 1.0) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.9e+28) || !(z <= 35000.0))
		tmp = Float64(x + Float64(a / Float64(Float64(Float64(t + 1.0) / z) + -1.0)));
	else
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(t + 1.0) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.9e+28) || ~((z <= 35000.0)))
		tmp = x + (a / (((t + 1.0) / z) + -1.0));
	else
		tmp = x + ((z - y) / ((t + 1.0) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.9e+28], N[Not[LessEqual[z, 35000.0]], $MachinePrecision]], N[(x + N[(a / N[(N[(N[(t + 1.0), $MachinePrecision] / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - y), $MachinePrecision] / N[(N[(t + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9000000000000001e28 or 35000 < 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 y around 0 69.4%

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

      1. mul-1-neg 69.4%

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

      2. *-commutative 69.4%

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

      3. associate--l+ 69.4%

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

      4. +-commutative 69.4%

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

      5. associate-*r/ 88.3%

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

      6. distribute-rgt-neg-in 88.3%

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

      7. distribute-neg-frac 88.3%

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

      8. +-commutative 88.3%

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

   7. Simplified 88.3%

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

   8. Taylor expanded in x around 0 69.4%

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

      1. +-commutative 69.4%

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

      2. associate-/l* 91.9%

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

      3. sub-neg 91.9%

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

      4. associate-+r+ 91.9%

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

      5. mul-1-neg 91.9%

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

      6. +-commutative 91.9%

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

      7. mul-1-neg 91.9%

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

      8. sub-neg 91.9%

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

      9. associate--r- 91.9%

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

      10. sub-neg 91.9%

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

      11. metadata-eval 91.9%

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

   10. Simplified 91.9%

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

   11. Taylor expanded in a around 0 69.4%

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

       1. associate-/l* 91.9%

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

       2. div-sub 91.9%

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

       3. *-inverses 91.9%

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

   13. Simplified 91.9%

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

   if -2.9000000000000001e28 < z < 35000

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 97.1%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+28} \lor \neg \left(z \leq 35000\right):\\ \;\;\;\;x + \frac{a}{\frac{t + 1}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{t + 1}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+55} \lor \neg \left(z \leq 4.3 \cdot 10^{+45}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e+55) (not (<= z 4.3e+45)))
   (+ 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 <= -1.9e+55) || !(z <= 4.3e+45)) {
		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 <= (-1.9d+55)) .or. (.not. (z <= 4.3d+45))) 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 <= -1.9e+55) || !(z <= 4.3e+45)) {
		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 <= -1.9e+55) or not (z <= 4.3e+45):
		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 <= -1.9e+55) || !(z <= 4.3e+45))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(-z) / a)));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.9e+55) || ~((z <= 4.3e+45)))
		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, -1.9e+55], N[Not[LessEqual[z, 4.3e+45]], $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 < -1.9e55 or 4.3000000000000003e45 < z

   1. Initial program 93.7%

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

   3. Taylor expanded in z around inf 82.2%

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

      1. mul-1-neg 82.2%

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

   5. Simplified 82.2%

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

   if -1.9e55 < z < 4.3000000000000003e45

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 88.7%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+55} \lor \neg \left(z \leq 4.3 \cdot 10^{+45}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+142} \lor \neg \left(z \leq 6.8 \cdot 10^{+45}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e+142) (not (<= z 6.8e+45)))
   (- 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 <= -7.2e+142) || !(z <= 6.8e+45)) {
		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 <= (-7.2d+142)) .or. (.not. (z <= 6.8d+45))) 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 <= -7.2e+142) || !(z <= 6.8e+45)) {
		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 <= -7.2e+142) or not (z <= 6.8e+45):
		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 <= -7.2e+142) || !(z <= 6.8e+45))
		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 <= -7.2e+142) || ~((z <= 6.8e+45)))
		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, -7.2e+142], N[Not[LessEqual[z, 6.8e+45]], $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 < -7.2000000000000003e142 or 6.8e45 < z

   1. Initial program 92.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 81.9%

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

   if -7.2000000000000003e142 < z < 6.8e45

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. 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 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+142} \lor \neg \left(z \leq 6.8 \cdot 10^{+45}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+142} \lor \neg \left(z \leq 2.25 \cdot 10^{+170}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e+142) (not (<= z 2.25e+170))) (- x a) (+ x (* z (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e+142) || !(z <= 2.25e+170)) {
		tmp = x - a;
	} else {
		tmp = x + (z * (a / 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 <= (-4.8d+142)) .or. (.not. (z <= 2.25d+170))) then
        tmp = x - a
    else
        tmp = x + (z * (a / 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 <= -4.8e+142) || !(z <= 2.25e+170)) {
		tmp = x - a;
	} else {
		tmp = x + (z * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e+142) or not (z <= 2.25e+170):
		tmp = x - a
	else:
		tmp = x + (z * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e+142) || !(z <= 2.25e+170))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(z * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.8e+142) || ~((z <= 2.25e+170)))
		tmp = x - a;
	else
		tmp = x + (z * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.8e+142], N[Not[LessEqual[z, 2.25e+170]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(z * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7999999999999998e142 or 2.25000000000000011e170 < z

   1. Initial program 90.8%

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

      1. associate-/r/ 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 86.2%

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

   if -4.7999999999999998e142 < z < 2.25000000000000011e170

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 61.0%

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

      1. associate-/l* 62.9%

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

   7. Simplified 62.9%

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

   8. Taylor expanded in y around 0 60.0%

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

      1. mul-1-neg 60.0%

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

   10. Simplified 60.0%

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

   11. Taylor expanded in x around 0 59.2%

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

       1. associate-/l* 60.0%

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

       2. associate-/r/ 59.9%

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

   13. Simplified 59.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+142} \lor \neg \left(z \leq 2.25 \cdot 10^{+170}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+129} \lor \neg \left(z \leq 3.4 \cdot 10^{+47}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.8e+129) (not (<= z 3.4e+47))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+129) || !(z <= 3.4e+47)) {
		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 <= (-8.8d+129)) .or. (.not. (z <= 3.4d+47))) 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 <= -8.8e+129) || !(z <= 3.4e+47)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.8e+129) or not (z <= 3.4e+47):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.8e+129) || !(z <= 3.4e+47))
		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 <= -8.8e+129) || ~((z <= 3.4e+47)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.8e+129], N[Not[LessEqual[z, 3.4e+47]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.7999999999999997e129 or 3.3999999999999998e47 < z

   1. Initial program 92.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 81.9%

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

   if -8.7999999999999997e129 < z < 3.3999999999999998e47

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 58.1%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+129} \lor \neg \left(z \leq 3.4 \cdot 10^{+47}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.2 \cdot 10^{+206}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 4.2e+206) x (- a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 4.2e+206) {
		tmp = x;
	} else {
		tmp = -a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 4.2d+206) then
        tmp = x
    else
        tmp = -a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 4.2e+206) {
		tmp = x;
	} else {
		tmp = -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 4.2e+206:
		tmp = x
	else:
		tmp = -a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 4.2e+206)
		tmp = x;
	else
		tmp = Float64(-a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 4.2e+206)
		tmp = x;
	else
		tmp = -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 4.2e+206], x, (-a)]

Derivation

1. Split input into 2 regimes

2. if a < 4.19999999999999974e206

   1. Initial program 96.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 x around inf 60.9%

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

   if 4.19999999999999974e206 < a

   1. Initial program 99.8%

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

      1. associate-/r/ 99.8%

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

   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 0 18.2%

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

      1. mul-1-neg 18.2%

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

      2. *-commutative 18.2%

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

      3. associate--l+ 18.2%

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

      4. +-commutative 18.2%

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

      5. associate-*r/ 72.3%

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

      6. distribute-rgt-neg-in 72.3%

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

      7. distribute-neg-frac 72.3%

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

      8. +-commutative 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in x around 0 9.9%

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

   9. Taylor expanded in z around inf 44.4%

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

       1. neg-mul-1 44.4%

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

   11. Simplified 44.4%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.2 \cdot 10^{+206}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.3% 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 96.9%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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 x around inf 55.9%

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

6. Final simplification 55.9%

   \[\leadsto x \]
7. 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 2024034 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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