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

Percentage Accurate: 97.1% → 99.7%

Time: 14.1s

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: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) - (t - z))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. associate-/r/ 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{t} \cdot \left(z - y\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -5.7 \cdot 10^{+47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-139}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ a t) (- z y)))) (t_2 (+ x (* (- y z) (/ a z)))))
   (if (<= z -5.7e+47)
     t_2
     (if (<= z -1.9e-110)
       t_1
       (if (<= z 1.42e-139) (- x (* y a)) (if (<= z 1.05e+63) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a / t) * (z - y));
	double t_2 = x + ((y - z) * (a / z));
	double tmp;
	if (z <= -5.7e+47) {
		tmp = t_2;
	} else if (z <= -1.9e-110) {
		tmp = t_1;
	} else if (z <= 1.42e-139) {
		tmp = x - (y * a);
	} else if (z <= 1.05e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x + ((a / t) * (z - y))
    t_2 = x + ((y - z) * (a / z))
    if (z <= (-5.7d+47)) then
        tmp = t_2
    else if (z <= (-1.9d-110)) then
        tmp = t_1
    else if (z <= 1.42d-139) then
        tmp = x - (y * a)
    else if (z <= 1.05d+63) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a / t) * (z - y));
	double t_2 = x + ((y - z) * (a / z));
	double tmp;
	if (z <= -5.7e+47) {
		tmp = t_2;
	} else if (z <= -1.9e-110) {
		tmp = t_1;
	} else if (z <= 1.42e-139) {
		tmp = x - (y * a);
	} else if (z <= 1.05e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((a / t) * (z - y))
	t_2 = x + ((y - z) * (a / z))
	tmp = 0
	if z <= -5.7e+47:
		tmp = t_2
	elif z <= -1.9e-110:
		tmp = t_1
	elif z <= 1.42e-139:
		tmp = x - (y * a)
	elif z <= 1.05e+63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(a / t) * Float64(z - y)))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(a / z)))
	tmp = 0.0
	if (z <= -5.7e+47)
		tmp = t_2;
	elseif (z <= -1.9e-110)
		tmp = t_1;
	elseif (z <= 1.42e-139)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 1.05e+63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((a / t) * (z - y));
	t_2 = x + ((y - z) * (a / z));
	tmp = 0.0;
	if (z <= -5.7e+47)
		tmp = t_2;
	elseif (z <= -1.9e-110)
		tmp = t_1;
	elseif (z <= 1.42e-139)
		tmp = x - (y * a);
	elseif (z <= 1.05e+63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.7e+47], t$95$2, If[LessEqual[z, -1.9e-110], t$95$1, If[LessEqual[z, 1.42e-139], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+63], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6999999999999997e47 or 1.0500000000000001e63 < z

   1. Initial program 94.8%

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

   3. Taylor expanded in z around inf 87.7%

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

      1. associate-*r/ 87.7%

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

      2. neg-mul-1 87.7%

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

   5. Simplified 87.7%

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

      1. div-sub 87.7%

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

      2. div-inv 87.7%

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

      3. clear-num 87.8%

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

      4. add-sqr-sqrt 48.0%

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

      5. sqrt-unprod 78.1%

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

      6. sqr-neg 78.1%

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

      7. sqrt-unprod 33.2%

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

      8. add-sqr-sqrt 72.6%

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

      9. div-inv 72.6%

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

      10. clear-num 72.6%

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

      11. add-sqr-sqrt 39.3%

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

      12. sqrt-unprod 52.9%

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

      13. sqr-neg 52.9%

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

      14. sqrt-unprod 24.9%

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

      15. add-sqr-sqrt 49.3%

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

   7. Applied egg-rr 49.3%

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

      1. distribute-rgt-out-- 49.3%

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

   9. Simplified 49.3%

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

       1. cancel-sign-sub-inv 49.3%

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

       2. distribute-neg-frac 49.3%

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

       3. add-sqr-sqrt 33.5%

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

       4. sqrt-unprod 62.9%

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

       5. sqr-neg 62.9%

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

       6. sqrt-unprod 39.5%

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

       7. add-sqr-sqrt 87.8%

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

   11. Applied egg-rr 87.8%

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

   if -5.6999999999999997e47 < z < -1.8999999999999999e-110 or 1.41999999999999997e-139 < z < 1.0500000000000001e63

   1. Initial program 97.7%

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

   3. Taylor expanded in t around inf 80.0%

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

   4. Taylor expanded in y around 0 77.5%

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

      1. +-commutative 77.5%

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

      2. *-commutative 77.5%

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

      3. associate-*r/ 78.7%

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

      4. mul-1-neg 78.7%

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

      5. *-commutative 78.7%

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

      6. associate-*r/ 78.7%

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

      7. sub-neg 78.7%

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

      8. distribute-rgt-out-- 80.0%

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

   6. Simplified 80.0%

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

   if -1.8999999999999999e-110 < z < 1.41999999999999997e-139

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around 0 96.8%

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

   6. Taylor expanded in t around 0 81.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+47}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-139}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+63}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-141}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+49}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ a z)))))
   (if (<= z -1.05)
     t_1
     (if (<= z 1.4e-141)
       (- x (* y a))
       (if (<= z 5.2e+49) (- x (* y (/ a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (a / z));
	double tmp;
	if (z <= -1.05) {
		tmp = t_1;
	} else if (z <= 1.4e-141) {
		tmp = x - (y * a);
	} else if (z <= 5.2e+49) {
		tmp = x - (y * (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * (a / z))
    if (z <= (-1.05d0)) then
        tmp = t_1
    else if (z <= 1.4d-141) then
        tmp = x - (y * a)
    else if (z <= 5.2d+49) then
        tmp = x - (y * (a / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (a / z));
	double tmp;
	if (z <= -1.05) {
		tmp = t_1;
	} else if (z <= 1.4e-141) {
		tmp = x - (y * a);
	} else if (z <= 5.2e+49) {
		tmp = x - (y * (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (a / z))
	tmp = 0
	if z <= -1.05:
		tmp = t_1
	elif z <= 1.4e-141:
		tmp = x - (y * a)
	elif z <= 5.2e+49:
		tmp = x - (y * (a / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(a / z)))
	tmp = 0.0
	if (z <= -1.05)
		tmp = t_1;
	elseif (z <= 1.4e-141)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 5.2e+49)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (a / z));
	tmp = 0.0;
	if (z <= -1.05)
		tmp = t_1;
	elseif (z <= 1.4e-141)
		tmp = x - (y * a);
	elseif (z <= 5.2e+49)
		tmp = x - (y * (a / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05], t$95$1, If[LessEqual[z, 1.4e-141], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+49], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000004 or 5.19999999999999977e49 < z

   1. Initial program 94.5%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. associate-*r/ 83.8%

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

      2. neg-mul-1 83.8%

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

   5. Simplified 83.8%

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

      1. div-sub 83.8%

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

      2. div-inv 83.8%

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

      3. clear-num 83.9%

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

      4. add-sqr-sqrt 47.3%

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

      5. sqrt-unprod 75.5%

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

      6. sqr-neg 75.5%

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

      7. sqrt-unprod 30.8%

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

      8. add-sqr-sqrt 68.8%

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

      9. div-inv 68.7%

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

      10. clear-num 68.8%

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

      11. add-sqr-sqrt 37.9%

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

      12. sqrt-unprod 51.7%

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

      13. sqr-neg 51.7%

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

      14. sqrt-unprod 23.5%

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

      15. add-sqr-sqrt 48.6%

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

   7. Applied egg-rr 48.6%

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

      1. distribute-rgt-out-- 48.6%

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

   9. Simplified 48.6%

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

       1. cancel-sign-sub-inv 48.6%

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

       2. distribute-neg-frac 48.6%

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

       3. add-sqr-sqrt 31.9%

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

       4. sqrt-unprod 61.1%

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

       5. sqr-neg 61.1%

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

       6. sqrt-unprod 37.9%

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

       7. add-sqr-sqrt 83.8%

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

   11. Applied egg-rr 83.8%

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

   if -1.05000000000000004 < z < 1.40000000000000006e-141

   1. Initial program 99.8%

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

      1. associate-/r/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around 0 95.5%

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

   6. Taylor expanded in t around 0 78.6%

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

   if 1.40000000000000006e-141 < z < 5.19999999999999977e49

   1. Initial program 98.0%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 78.8%

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

   6. Taylor expanded in t around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-*r/ 72.7%

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

   8. Simplified 72.7%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-141}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+49}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -6.7 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 45:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+63}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ a z)))))
   (if (<= z -6.7e+48)
     t_1
     (if (<= z 45.0)
       (+ x (* a (/ y (- -1.0 t))))
       (if (<= z 1.5e+63) (- x (* (- y z) (/ a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (a / z));
	double tmp;
	if (z <= -6.7e+48) {
		tmp = t_1;
	} else if (z <= 45.0) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 1.5e+63) {
		tmp = x - ((y - z) * (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * (a / z))
    if (z <= (-6.7d+48)) then
        tmp = t_1
    else if (z <= 45.0d0) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else if (z <= 1.5d+63) then
        tmp = x - ((y - z) * (a / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (a / z));
	double tmp;
	if (z <= -6.7e+48) {
		tmp = t_1;
	} else if (z <= 45.0) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 1.5e+63) {
		tmp = x - ((y - z) * (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (a / z))
	tmp = 0
	if z <= -6.7e+48:
		tmp = t_1
	elif z <= 45.0:
		tmp = x + (a * (y / (-1.0 - t)))
	elif z <= 1.5e+63:
		tmp = x - ((y - z) * (a / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(a / z)))
	tmp = 0.0
	if (z <= -6.7e+48)
		tmp = t_1;
	elseif (z <= 45.0)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	elseif (z <= 1.5e+63)
		tmp = Float64(x - Float64(Float64(y - z) * Float64(a / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (a / z));
	tmp = 0.0;
	if (z <= -6.7e+48)
		tmp = t_1;
	elseif (z <= 45.0)
		tmp = x + (a * (y / (-1.0 - t)));
	elseif (z <= 1.5e+63)
		tmp = x - ((y - z) * (a / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.7e+48], t$95$1, If[LessEqual[z, 45.0], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+63], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.7e48 or 1.5e63 < z

   1. Initial program 94.7%

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

   3. Taylor expanded in z around inf 87.6%

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

      1. associate-*r/ 87.6%

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

      2. neg-mul-1 87.6%

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

   5. Simplified 87.6%

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

      1. div-sub 87.6%

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

      2. div-inv 87.6%

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

      3. clear-num 87.7%

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

      4. add-sqr-sqrt 47.4%

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

      5. sqrt-unprod 77.9%

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

      6. sqr-neg 77.9%

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

      7. sqrt-unprod 33.6%

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

      8. add-sqr-sqrt 72.3%

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

      9. div-inv 72.3%

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

      10. clear-num 72.3%

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

      11. add-sqr-sqrt 38.6%

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

      12. sqrt-unprod 52.4%

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

      13. sqr-neg 52.4%

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

      14. sqrt-unprod 25.2%

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

      15. add-sqr-sqrt 48.7%

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

   7. Applied egg-rr 48.7%

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

      1. distribute-rgt-out-- 48.7%

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

   9. Simplified 48.7%

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

       1. cancel-sign-sub-inv 48.7%

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

       2. distribute-neg-frac 48.7%

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

       3. add-sqr-sqrt 33.9%

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

       4. sqrt-unprod 62.5%

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

       5. sqr-neg 62.5%

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

       6. sqrt-unprod 38.8%

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

       7. add-sqr-sqrt 87.6%

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

   11. Applied egg-rr 87.6%

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

   if -6.7e48 < z < 45

   1. Initial program 99.2%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 91.2%

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

   if 45 < z < 1.5e63

   1. Initial program 96.0%

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

   3. Taylor expanded in t around inf 84.1%

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

   4. Taylor expanded in y around 0 80.3%

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

      1. +-commutative 80.3%

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

      2. *-commutative 80.3%

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

      3. associate-*r/ 80.2%

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

      4. mul-1-neg 80.2%

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

      5. *-commutative 80.2%

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

      6. associate-*r/ 80.3%

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

      7. sub-neg 80.3%

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

      8. distribute-rgt-out-- 84.3%

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

   6. Simplified 84.3%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{+48}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 45:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+63}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0225:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+62}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ a z)))))
   (if (<= z -1.8e+49)
     t_1
     (if (<= z 0.0225)
       (+ x (* a (/ y (- -1.0 t))))
       (if (<= z 9.8e+62) (- x (* a (/ (- y z) t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (a / z));
	double tmp;
	if (z <= -1.8e+49) {
		tmp = t_1;
	} else if (z <= 0.0225) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 9.8e+62) {
		tmp = x - (a * ((y - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * (a / z))
    if (z <= (-1.8d+49)) then
        tmp = t_1
    else if (z <= 0.0225d0) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else if (z <= 9.8d+62) then
        tmp = x - (a * ((y - z) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (a / z));
	double tmp;
	if (z <= -1.8e+49) {
		tmp = t_1;
	} else if (z <= 0.0225) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 9.8e+62) {
		tmp = x - (a * ((y - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (a / z))
	tmp = 0
	if z <= -1.8e+49:
		tmp = t_1
	elif z <= 0.0225:
		tmp = x + (a * (y / (-1.0 - t)))
	elif z <= 9.8e+62:
		tmp = x - (a * ((y - z) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(a / z)))
	tmp = 0.0
	if (z <= -1.8e+49)
		tmp = t_1;
	elseif (z <= 0.0225)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	elseif (z <= 9.8e+62)
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (a / z));
	tmp = 0.0;
	if (z <= -1.8e+49)
		tmp = t_1;
	elseif (z <= 0.0225)
		tmp = x + (a * (y / (-1.0 - t)));
	elseif (z <= 9.8e+62)
		tmp = x - (a * ((y - z) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+49], t$95$1, If[LessEqual[z, 0.0225], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+62], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999998e49 or 9.7999999999999994e62 < z

   1. Initial program 94.7%

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

   3. Taylor expanded in z around inf 87.6%

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

      1. associate-*r/ 87.6%

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

      2. neg-mul-1 87.6%

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

   5. Simplified 87.6%

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

      1. div-sub 87.6%

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

      2. div-inv 87.6%

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

      3. clear-num 87.7%

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

      4. add-sqr-sqrt 47.4%

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

      5. sqrt-unprod 77.9%

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

      6. sqr-neg 77.9%

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

      7. sqrt-unprod 33.6%

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

      8. add-sqr-sqrt 72.3%

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

      9. div-inv 72.3%

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

      10. clear-num 72.3%

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

      11. add-sqr-sqrt 38.6%

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

      12. sqrt-unprod 52.4%

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

      13. sqr-neg 52.4%

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

      14. sqrt-unprod 25.2%

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

      15. add-sqr-sqrt 48.7%

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

   7. Applied egg-rr 48.7%

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

      1. distribute-rgt-out-- 48.7%

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

   9. Simplified 48.7%

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

       1. cancel-sign-sub-inv 48.7%

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

       2. distribute-neg-frac 48.7%

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

       3. add-sqr-sqrt 33.9%

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

       4. sqrt-unprod 62.5%

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

       5. sqr-neg 62.5%

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

       6. sqrt-unprod 38.8%

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

       7. add-sqr-sqrt 87.6%

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

   11. Applied egg-rr 87.6%

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

   if -1.79999999999999998e49 < z < 0.022499999999999999

   1. Initial program 99.2%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 91.2%

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

   if 0.022499999999999999 < z < 9.7999999999999994e62

   1. Initial program 96.0%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 88.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+49}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 0.0225:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+62}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(a - a \cdot \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.14 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 880:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+63}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (- a (* a (/ y z))))))
   (if (<= z -1.14e+48)
     t_1
     (if (<= z 880.0)
       (+ x (* a (/ y (- -1.0 t))))
       (if (<= z 1.1e+63) (- x (* a (/ (- y z) t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a - (a * (y / z)));
	double tmp;
	if (z <= -1.14e+48) {
		tmp = t_1;
	} else if (z <= 880.0) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 1.1e+63) {
		tmp = x - (a * ((y - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (a - (a * (y / z)))
    if (z <= (-1.14d+48)) then
        tmp = t_1
    else if (z <= 880.0d0) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else if (z <= 1.1d+63) then
        tmp = x - (a * ((y - z) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a - (a * (y / z)));
	double tmp;
	if (z <= -1.14e+48) {
		tmp = t_1;
	} else if (z <= 880.0) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else if (z <= 1.1e+63) {
		tmp = x - (a * ((y - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a - (a * (y / z)))
	tmp = 0
	if z <= -1.14e+48:
		tmp = t_1
	elif z <= 880.0:
		tmp = x + (a * (y / (-1.0 - t)))
	elif z <= 1.1e+63:
		tmp = x - (a * ((y - z) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a - Float64(a * Float64(y / z))))
	tmp = 0.0
	if (z <= -1.14e+48)
		tmp = t_1;
	elseif (z <= 880.0)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	elseif (z <= 1.1e+63)
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a - (a * (y / z)));
	tmp = 0.0;
	if (z <= -1.14e+48)
		tmp = t_1;
	elseif (z <= 880.0)
		tmp = x + (a * (y / (-1.0 - t)));
	elseif (z <= 1.1e+63)
		tmp = x - (a * ((y - z) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a - N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.14e+48], t$95$1, If[LessEqual[z, 880.0], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+63], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1399999999999999e48 or 1.0999999999999999e63 < z

   1. Initial program 94.7%

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

   3. Taylor expanded in z around inf 87.6%

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

      1. associate-*r/ 87.6%

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

      2. neg-mul-1 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in y around 0 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

      3. associate-/l* 91.8%

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

   8. Simplified 91.8%

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

   if -1.1399999999999999e48 < z < 880

   1. Initial program 99.2%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 91.2%

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

   if 880 < z < 1.0999999999999999e63

   1. Initial program 96.0%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 88.1%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+48}:\\ \;\;\;\;x - \left(a - a \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 880:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+63}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(a - a \cdot \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+25}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-138}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+62}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e+25)
   (- x a)
   (if (<= z 2.5e-138)
     (- x (* y a))
     (if (<= z 9.8e+62) (+ x (* a (/ z t))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+25) {
		tmp = x - a;
	} else if (z <= 2.5e-138) {
		tmp = x - (y * a);
	} else if (z <= 9.8e+62) {
		tmp = x + (a * (z / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.6d+25)) then
        tmp = x - a
    else if (z <= 2.5d-138) then
        tmp = x - (y * a)
    else if (z <= 9.8d+62) then
        tmp = x + (a * (z / t))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+25) {
		tmp = x - a;
	} else if (z <= 2.5e-138) {
		tmp = x - (y * a);
	} else if (z <= 9.8e+62) {
		tmp = x + (a * (z / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e+25:
		tmp = x - a
	elif z <= 2.5e-138:
		tmp = x - (y * a)
	elif z <= 9.8e+62:
		tmp = x + (a * (z / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e+25)
		tmp = Float64(x - a);
	elseif (z <= 2.5e-138)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 9.8e+62)
		tmp = Float64(x + Float64(a * Float64(z / t)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.6e+25)
		tmp = x - a;
	elseif (z <= 2.5e-138)
		tmp = x - (y * a);
	elseif (z <= 9.8e+62)
		tmp = x + (a * (z / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e+25], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.5e-138], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+62], N[(x + N[(a * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5999999999999996e25 or 9.7999999999999994e62 < z

   1. Initial program 94.9%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 76.7%

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

   if -4.5999999999999996e25 < z < 2.49999999999999994e-138

   1. Initial program 99.8%

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

      1. associate-/r/ 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   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 77.4%

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

   if 2.49999999999999994e-138 < z < 9.7999999999999994e62

   1. Initial program 96.5%

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

   3. Taylor expanded in t around inf 78.7%

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

   4. Taylor expanded in y around 0 61.5%

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

      1. sub-neg 61.5%

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

      2. mul-1-neg 61.5%

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

      3. remove-double-neg 61.5%

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

      4. associate-/l* 61.5%

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

   6. Simplified 61.5%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+25}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-138}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+62}:\\ \;\;\;\;x + a \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+17}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-140}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+49}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.8e+17)
   (- x a)
   (if (<= z 7.8e-140)
     (- x (* y a))
     (if (<= z 4.6e+49) (- x (* y (/ a t))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+17) {
		tmp = x - a;
	} else if (z <= 7.8e-140) {
		tmp = x - (y * a);
	} else if (z <= 4.6e+49) {
		tmp = x - (y * (a / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.8d+17)) then
        tmp = x - a
    else if (z <= 7.8d-140) then
        tmp = x - (y * a)
    else if (z <= 4.6d+49) then
        tmp = x - (y * (a / t))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e+17) {
		tmp = x - a;
	} else if (z <= 7.8e-140) {
		tmp = x - (y * a);
	} else if (z <= 4.6e+49) {
		tmp = x - (y * (a / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e+17:
		tmp = x - a
	elif z <= 7.8e-140:
		tmp = x - (y * a)
	elif z <= 4.6e+49:
		tmp = x - (y * (a / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e+17)
		tmp = Float64(x - a);
	elseif (z <= 7.8e-140)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 4.6e+49)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e+17)
		tmp = x - a;
	elseif (z <= 7.8e-140)
		tmp = x - (y * a);
	elseif (z <= 4.6e+49)
		tmp = x - (y * (a / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.8e+17], N[(x - a), $MachinePrecision], If[LessEqual[z, 7.8e-140], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+49], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.8e17 or 4.60000000000000004e49 < z

   1. Initial program 94.2%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 75.7%

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

   if -8.8e17 < z < 7.80000000000000038e-140

   1. Initial program 99.8%

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

      1. associate-/r/ 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   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 77.4%

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

   if 7.80000000000000038e-140 < z < 4.60000000000000004e49

   1. Initial program 98.0%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 78.8%

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

   6. Taylor expanded in t around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-*r/ 72.7%

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

   8. Simplified 72.7%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+17}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-140}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+49}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+18} \lor \neg \left(t \leq 7.2 \cdot 10^{+205}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z - 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8e+18) (not (<= t 7.2e+205)))
   (+ x (* a (/ (- z y) t)))
   (+ x (* a (/ (- y z) (- z 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e+18) || !(t <= 7.2e+205)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x + (a * ((y - z) / (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 <= (-8d+18)) .or. (.not. (t <= 7.2d+205))) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = x + (a * ((y - z) / (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 <= -8e+18) || !(t <= 7.2e+205)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x + (a * ((y - z) / (z - 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8e+18) or not (t <= 7.2e+205):
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x + (a * ((y - z) / (z - 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8e+18) || !(t <= 7.2e+205))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / Float64(z - 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8e+18) || ~((t <= 7.2e+205)))
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x + (a * ((y - z) / (z - 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8e+18], N[Not[LessEqual[t, 7.2e+205]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8e18 or 7.20000000000000003e205 < t

   1. Initial program 96.9%

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

      1. associate-/r/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around inf 92.2%

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

   if -8e18 < t < 7.20000000000000003e205

   1. Initial program 97.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around 0 94.7%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+18} \lor \neg \left(t \leq 7.2 \cdot 10^{+205}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z - 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+19} \lor \neg \left(z \leq 6.4 \cdot 10^{+22}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3e+19) (not (<= z 6.4e+22))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e+19) || !(z <= 6.4e+22)) {
		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 <= (-3d+19)) .or. (.not. (z <= 6.4d+22))) 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 <= -3e+19) || !(z <= 6.4e+22)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3e+19) or not (z <= 6.4e+22):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3e+19) || !(z <= 6.4e+22))
		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 <= -3e+19) || ~((z <= 6.4e+22)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3e+19], N[Not[LessEqual[z, 6.4e+22]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e19 or 6.4e22 < z

   1. Initial program 94.6%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 73.9%

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

   if -3e19 < z < 6.4e22

   1. Initial program 99.2%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 89.1%

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

   6. Taylor expanded in t around 0 70.7%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+19} \lor \neg \left(z \leq 6.4 \cdot 10^{+22}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -12500000000000 \lor \neg \left(z \leq 6.2 \cdot 10^{+24}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -12500000000000.0) (not (<= z 6.2e+24))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -12500000000000.0) || !(z <= 6.2e+24)) {
		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 <= (-12500000000000.0d0)) .or. (.not. (z <= 6.2d+24))) 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 <= -12500000000000.0) || !(z <= 6.2e+24)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -12500000000000.0) or not (z <= 6.2e+24):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -12500000000000.0) || !(z <= 6.2e+24))
		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 <= -12500000000000.0) || ~((z <= 6.2e+24)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -12500000000000.0], N[Not[LessEqual[z, 6.2e+24]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e13 or 6.20000000000000022e24 < z

   1. Initial program 94.5%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 74.6%

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

   if -1.25e13 < z < 6.20000000000000022e24

   1. Initial program 99.2%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 62.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12500000000000 \lor \neg \left(z \leq 6.2 \cdot 10^{+24}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. associate-/r/ 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around inf 58.0%

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

6. Final simplification 58.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024046 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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