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

Percentage Accurate: 97.1% → 99.6%

Time: 11.0s

Alternatives: 13

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: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

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

Alternative 2: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+81}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-120}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-233}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-260}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 51:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -2.8e+81)
     (- x a)
     (if (<= z -5.6e-27)
       (+ x (/ (* y a) z))
       (if (<= z -2.15e-120)
         (- x (* y (/ a t)))
         (if (<= z -6.8e-233)
           t_1
           (if (<= z 8e-260)
             (- x (/ a (/ t y)))
             (if (<= z 4.5e-82)
               t_1
               (if (<= z 51.0) (- x (/ y (/ t a))) (- x a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -2.8e+81) {
		tmp = x - a;
	} else if (z <= -5.6e-27) {
		tmp = x + ((y * a) / z);
	} else if (z <= -2.15e-120) {
		tmp = x - (y * (a / t));
	} else if (z <= -6.8e-233) {
		tmp = t_1;
	} else if (z <= 8e-260) {
		tmp = x - (a / (t / y));
	} else if (z <= 4.5e-82) {
		tmp = t_1;
	} else if (z <= 51.0) {
		tmp = x - (y / (t / a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * a)
    if (z <= (-2.8d+81)) then
        tmp = x - a
    else if (z <= (-5.6d-27)) then
        tmp = x + ((y * a) / z)
    else if (z <= (-2.15d-120)) then
        tmp = x - (y * (a / t))
    else if (z <= (-6.8d-233)) then
        tmp = t_1
    else if (z <= 8d-260) then
        tmp = x - (a / (t / y))
    else if (z <= 4.5d-82) then
        tmp = t_1
    else if (z <= 51.0d0) then
        tmp = x - (y / (t / a))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -2.8e+81) {
		tmp = x - a;
	} else if (z <= -5.6e-27) {
		tmp = x + ((y * a) / z);
	} else if (z <= -2.15e-120) {
		tmp = x - (y * (a / t));
	} else if (z <= -6.8e-233) {
		tmp = t_1;
	} else if (z <= 8e-260) {
		tmp = x - (a / (t / y));
	} else if (z <= 4.5e-82) {
		tmp = t_1;
	} else if (z <= 51.0) {
		tmp = x - (y / (t / a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	tmp = 0
	if z <= -2.8e+81:
		tmp = x - a
	elif z <= -5.6e-27:
		tmp = x + ((y * a) / z)
	elif z <= -2.15e-120:
		tmp = x - (y * (a / t))
	elif z <= -6.8e-233:
		tmp = t_1
	elif z <= 8e-260:
		tmp = x - (a / (t / y))
	elif z <= 4.5e-82:
		tmp = t_1
	elif z <= 51.0:
		tmp = x - (y / (t / a))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (z <= -2.8e+81)
		tmp = Float64(x - a);
	elseif (z <= -5.6e-27)
		tmp = Float64(x + Float64(Float64(y * a) / z));
	elseif (z <= -2.15e-120)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	elseif (z <= -6.8e-233)
		tmp = t_1;
	elseif (z <= 8e-260)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (z <= 4.5e-82)
		tmp = t_1;
	elseif (z <= 51.0)
		tmp = Float64(x - Float64(y / Float64(t / a)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	tmp = 0.0;
	if (z <= -2.8e+81)
		tmp = x - a;
	elseif (z <= -5.6e-27)
		tmp = x + ((y * a) / z);
	elseif (z <= -2.15e-120)
		tmp = x - (y * (a / t));
	elseif (z <= -6.8e-233)
		tmp = t_1;
	elseif (z <= 8e-260)
		tmp = x - (a / (t / y));
	elseif (z <= 4.5e-82)
		tmp = t_1;
	elseif (z <= 51.0)
		tmp = x - (y / (t / a));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+81], N[(x - a), $MachinePrecision], If[LessEqual[z, -5.6e-27], N[(x + N[(N[(y * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.15e-120], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.8e-233], t$95$1, If[LessEqual[z, 8e-260], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-82], t$95$1, If[LessEqual[z, 51.0], N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.79999999999999995e81 or 51 < 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 79.0%

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

   if -2.79999999999999995e81 < z < -5.5999999999999999e-27

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. distribute-neg-frac2 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in y around inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-/l* 68.0%

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

      3. distribute-rgt-neg-in 68.0%

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

   8. Simplified 68.0%

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

      1. sub-neg 68.0%

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

      2. distribute-rgt-neg-out 68.0%

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

      3. remove-double-neg 68.0%

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

      4. div-inv 68.0%

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

      5. associate-*r* 68.0%

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

      6. add-sqr-sqrt 31.0%

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

      7. sqrt-unprod 49.3%

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

      8. sqr-neg 49.3%

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

      9. sqrt-unprod 33.3%

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

      10. add-sqr-sqrt 42.8%

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

      11. div-inv 42.8%

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

      12. add-sqr-sqrt 33.3%

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

      13. sqrt-unprod 49.3%

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

      14. sqr-neg 49.3%

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

      15. sqrt-unprod 31.0%

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

      16. add-sqr-sqrt 68.1%

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

      17. *-commutative 68.1%

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

   10. Applied egg-rr 68.1%

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

   if -5.5999999999999999e-27 < z < -2.14999999999999991e-120

   1. Initial program 99.8%

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

      1. associate-/r/ 99.9%

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

   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 72.6%

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

   6. Taylor expanded in y around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. clear-num 68.3%

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

      3. un-div-inv 68.3%

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

   8. Applied egg-rr 68.3%

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

      1. associate-/r/ 68.4%

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

   10. Simplified 68.4%

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

   if -2.14999999999999991e-120 < z < -6.8000000000000004e-233 or 7.99999999999999969e-260 < z < 4.4999999999999998e-82

   1. Initial program 98.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-/l* 95.5%

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

   7. Simplified 95.5%

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

   8. Taylor expanded in t around 0 88.0%

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

   if -6.8000000000000004e-233 < z < 7.99999999999999969e-260

   1. Initial program 100.0%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 99.8%

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

   6. Taylor expanded in y around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.9%

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

      3. un-div-inv 100.0%

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

   8. Applied egg-rr 100.0%

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

   if 4.4999999999999998e-82 < z < 51

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 90.1%

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

   6. Taylor expanded in t around inf 90.0%

      \[\leadsto x - \frac{y}{\color{blue}{\frac{t}{a}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+81}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-120}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-233}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-260}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-82}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 51:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ \mathbf{if}\;z \leq -3 \cdot 10^{+84}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-117}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-260}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))))
   (if (<= z -3e+84)
     (- x a)
     (if (<= z -3.7e-25)
       (+ x (/ (* y a) z))
       (if (<= z -2.65e-117)
         (- x (* y (/ a t)))
         (if (<= z -1.65e-232)
           t_1
           (if (<= z 1.35e-260)
             (- x (/ a (/ t y)))
             (if (<= z 4.7e-82)
               t_1
               (if (<= z 8.5) (- x (* a (/ y t))) (- x a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double tmp;
	if (z <= -3e+84) {
		tmp = x - a;
	} else if (z <= -3.7e-25) {
		tmp = x + ((y * a) / z);
	} else if (z <= -2.65e-117) {
		tmp = x - (y * (a / t));
	} else if (z <= -1.65e-232) {
		tmp = t_1;
	} else if (z <= 1.35e-260) {
		tmp = x - (a / (t / y));
	} else if (z <= 4.7e-82) {
		tmp = t_1;
	} else if (z <= 8.5) {
		tmp = x - (a * (y / 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) :: t_1
    real(8) :: tmp
    t_1 = x - (y * a)
    if (z <= (-3d+84)) then
        tmp = x - a
    else if (z <= (-3.7d-25)) then
        tmp = x + ((y * a) / z)
    else if (z <= (-2.65d-117)) then
        tmp = x - (y * (a / t))
    else if (z <= (-1.65d-232)) then
        tmp = t_1
    else if (z <= 1.35d-260) then
        tmp = x - (a / (t / y))
    else if (z <= 4.7d-82) then
        tmp = t_1
    else if (z <= 8.5d0) then
        tmp = x - (a * (y / 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 t_1 = x - (y * a);
	double tmp;
	if (z <= -3e+84) {
		tmp = x - a;
	} else if (z <= -3.7e-25) {
		tmp = x + ((y * a) / z);
	} else if (z <= -2.65e-117) {
		tmp = x - (y * (a / t));
	} else if (z <= -1.65e-232) {
		tmp = t_1;
	} else if (z <= 1.35e-260) {
		tmp = x - (a / (t / y));
	} else if (z <= 4.7e-82) {
		tmp = t_1;
	} else if (z <= 8.5) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	tmp = 0
	if z <= -3e+84:
		tmp = x - a
	elif z <= -3.7e-25:
		tmp = x + ((y * a) / z)
	elif z <= -2.65e-117:
		tmp = x - (y * (a / t))
	elif z <= -1.65e-232:
		tmp = t_1
	elif z <= 1.35e-260:
		tmp = x - (a / (t / y))
	elif z <= 4.7e-82:
		tmp = t_1
	elif z <= 8.5:
		tmp = x - (a * (y / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (z <= -3e+84)
		tmp = Float64(x - a);
	elseif (z <= -3.7e-25)
		tmp = Float64(x + Float64(Float64(y * a) / z));
	elseif (z <= -2.65e-117)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	elseif (z <= -1.65e-232)
		tmp = t_1;
	elseif (z <= 1.35e-260)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (z <= 4.7e-82)
		tmp = t_1;
	elseif (z <= 8.5)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	tmp = 0.0;
	if (z <= -3e+84)
		tmp = x - a;
	elseif (z <= -3.7e-25)
		tmp = x + ((y * a) / z);
	elseif (z <= -2.65e-117)
		tmp = x - (y * (a / t));
	elseif (z <= -1.65e-232)
		tmp = t_1;
	elseif (z <= 1.35e-260)
		tmp = x - (a / (t / y));
	elseif (z <= 4.7e-82)
		tmp = t_1;
	elseif (z <= 8.5)
		tmp = x - (a * (y / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+84], N[(x - a), $MachinePrecision], If[LessEqual[z, -3.7e-25], N[(x + N[(N[(y * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.65e-117], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.65e-232], t$95$1, If[LessEqual[z, 1.35e-260], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e-82], t$95$1, If[LessEqual[z, 8.5], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.99999999999999996e84 or 8.5 < 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 79.0%

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

   if -2.99999999999999996e84 < z < -3.70000000000000009e-25

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. distribute-neg-frac2 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in y around inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-/l* 68.0%

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

      3. distribute-rgt-neg-in 68.0%

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

   8. Simplified 68.0%

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

      1. sub-neg 68.0%

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

      2. distribute-rgt-neg-out 68.0%

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

      3. remove-double-neg 68.0%

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

      4. div-inv 68.0%

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

      5. associate-*r* 68.0%

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

      6. add-sqr-sqrt 31.0%

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

      7. sqrt-unprod 49.3%

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

      8. sqr-neg 49.3%

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

      9. sqrt-unprod 33.3%

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

      10. add-sqr-sqrt 42.8%

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

      11. div-inv 42.8%

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

      12. add-sqr-sqrt 33.3%

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

      13. sqrt-unprod 49.3%

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

      14. sqr-neg 49.3%

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

      15. sqrt-unprod 31.0%

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

      16. add-sqr-sqrt 68.1%

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

      17. *-commutative 68.1%

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

   10. Applied egg-rr 68.1%

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

   if -3.70000000000000009e-25 < z < -2.64999999999999993e-117

   1. Initial program 99.8%

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

      1. associate-/r/ 99.9%

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

   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 72.6%

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

   6. Taylor expanded in y around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. clear-num 68.3%

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

      3. un-div-inv 68.3%

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

   8. Applied egg-rr 68.3%

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

      1. associate-/r/ 68.4%

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

   10. Simplified 68.4%

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

   if -2.64999999999999993e-117 < z < -1.64999999999999993e-232 or 1.35000000000000003e-260 < z < 4.7000000000000001e-82

   1. Initial program 98.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-/l* 95.5%

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

   7. Simplified 95.5%

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

   8. Taylor expanded in t around 0 88.0%

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

   if -1.64999999999999993e-232 < z < 1.35000000000000003e-260

   1. Initial program 100.0%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 99.8%

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

   6. Taylor expanded in y around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.9%

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

      3. un-div-inv 100.0%

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

   8. Applied egg-rr 100.0%

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

   if 4.7000000000000001e-82 < z < 8.5

   1. Initial program 100.0%

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

      1. associate-/r/ 99.9%

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

   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 94.8%

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

   6. Taylor expanded in y around inf 89.9%

      \[\leadsto x - \color{blue}{\frac{y}{t}} \cdot a \]
3. Recombined 6 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+84}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-117}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-232}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-260}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-82}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 8.5:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{a}{t}\\ t_2 := x - y \cdot a\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+83}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-263}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 210:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ a t)))) (t_2 (- x (* y a))))
   (if (<= z -8.2e+83)
     (- x a)
     (if (<= z -3.8e-25)
       (+ x (/ (* y a) z))
       (if (<= z -2.65e-117)
         t_1
         (if (<= z -1.25e-263)
           t_2
           (if (<= z 1.36e-260)
             t_1
             (if (<= z 1.55e-85)
               t_2
               (if (<= z 210.0) (- x (* a (/ y t))) (- x a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (a / t));
	double t_2 = x - (y * a);
	double tmp;
	if (z <= -8.2e+83) {
		tmp = x - a;
	} else if (z <= -3.8e-25) {
		tmp = x + ((y * a) / z);
	} else if (z <= -2.65e-117) {
		tmp = t_1;
	} else if (z <= -1.25e-263) {
		tmp = t_2;
	} else if (z <= 1.36e-260) {
		tmp = t_1;
	} else if (z <= 1.55e-85) {
		tmp = t_2;
	} else if (z <= 210.0) {
		tmp = x - (a * (y / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * (a / t))
    t_2 = x - (y * a)
    if (z <= (-8.2d+83)) then
        tmp = x - a
    else if (z <= (-3.8d-25)) then
        tmp = x + ((y * a) / z)
    else if (z <= (-2.65d-117)) then
        tmp = t_1
    else if (z <= (-1.25d-263)) then
        tmp = t_2
    else if (z <= 1.36d-260) then
        tmp = t_1
    else if (z <= 1.55d-85) then
        tmp = t_2
    else if (z <= 210.0d0) then
        tmp = x - (a * (y / 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 t_1 = x - (y * (a / t));
	double t_2 = x - (y * a);
	double tmp;
	if (z <= -8.2e+83) {
		tmp = x - a;
	} else if (z <= -3.8e-25) {
		tmp = x + ((y * a) / z);
	} else if (z <= -2.65e-117) {
		tmp = t_1;
	} else if (z <= -1.25e-263) {
		tmp = t_2;
	} else if (z <= 1.36e-260) {
		tmp = t_1;
	} else if (z <= 1.55e-85) {
		tmp = t_2;
	} else if (z <= 210.0) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (a / t))
	t_2 = x - (y * a)
	tmp = 0
	if z <= -8.2e+83:
		tmp = x - a
	elif z <= -3.8e-25:
		tmp = x + ((y * a) / z)
	elif z <= -2.65e-117:
		tmp = t_1
	elif z <= -1.25e-263:
		tmp = t_2
	elif z <= 1.36e-260:
		tmp = t_1
	elif z <= 1.55e-85:
		tmp = t_2
	elif z <= 210.0:
		tmp = x - (a * (y / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(a / t)))
	t_2 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (z <= -8.2e+83)
		tmp = Float64(x - a);
	elseif (z <= -3.8e-25)
		tmp = Float64(x + Float64(Float64(y * a) / z));
	elseif (z <= -2.65e-117)
		tmp = t_1;
	elseif (z <= -1.25e-263)
		tmp = t_2;
	elseif (z <= 1.36e-260)
		tmp = t_1;
	elseif (z <= 1.55e-85)
		tmp = t_2;
	elseif (z <= 210.0)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (a / t));
	t_2 = x - (y * a);
	tmp = 0.0;
	if (z <= -8.2e+83)
		tmp = x - a;
	elseif (z <= -3.8e-25)
		tmp = x + ((y * a) / z);
	elseif (z <= -2.65e-117)
		tmp = t_1;
	elseif (z <= -1.25e-263)
		tmp = t_2;
	elseif (z <= 1.36e-260)
		tmp = t_1;
	elseif (z <= 1.55e-85)
		tmp = t_2;
	elseif (z <= 210.0)
		tmp = x - (a * (y / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+83], N[(x - a), $MachinePrecision], If[LessEqual[z, -3.8e-25], N[(x + N[(N[(y * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.65e-117], t$95$1, If[LessEqual[z, -1.25e-263], t$95$2, If[LessEqual[z, 1.36e-260], t$95$1, If[LessEqual[z, 1.55e-85], t$95$2, If[LessEqual[z, 210.0], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.2000000000000002e83 or 210 < 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 79.0%

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

   if -8.2000000000000002e83 < z < -3.7999999999999998e-25

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. distribute-neg-frac2 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in y around inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-/l* 68.0%

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

      3. distribute-rgt-neg-in 68.0%

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

   8. Simplified 68.0%

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

      1. sub-neg 68.0%

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

      2. distribute-rgt-neg-out 68.0%

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

      3. remove-double-neg 68.0%

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

      4. div-inv 68.0%

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

      5. associate-*r* 68.0%

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

      6. add-sqr-sqrt 31.0%

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

      7. sqrt-unprod 49.3%

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

      8. sqr-neg 49.3%

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

      9. sqrt-unprod 33.3%

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

      10. add-sqr-sqrt 42.8%

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

      11. div-inv 42.8%

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

      12. add-sqr-sqrt 33.3%

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

      13. sqrt-unprod 49.3%

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

      14. sqr-neg 49.3%

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

      15. sqrt-unprod 31.0%

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

      16. add-sqr-sqrt 68.1%

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

      17. *-commutative 68.1%

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

   10. Applied egg-rr 68.1%

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

   if -3.7999999999999998e-25 < z < -2.64999999999999993e-117 or -1.25000000000000002e-263 < z < 1.36e-260

   1. Initial program 99.9%

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

      1. associate-/r/ 99.8%

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

   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 81.9%

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

   6. Taylor expanded in y around inf 79.2%

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

      1. *-commutative 79.2%

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

      2. clear-num 79.1%

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

      3. un-div-inv 79.2%

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

   8. Applied egg-rr 79.2%

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

      1. associate-/r/ 79.2%

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

   10. Simplified 79.2%

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

   if -2.64999999999999993e-117 < z < -1.25000000000000002e-263 or 1.36e-260 < z < 1.5500000000000001e-85

   1. Initial program 98.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 94.4%

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

      1. *-commutative 94.4%

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

      2. associate-/l* 95.8%

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

   7. Simplified 95.8%

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

   8. Taylor expanded in t around 0 88.7%

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

   if 1.5500000000000001e-85 < z < 210

   1. Initial program 100.0%

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

      1. associate-/r/ 99.9%

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

   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 94.8%

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

   6. Taylor expanded in y around inf 89.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+83}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{-117}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-263}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-260}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-85}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 210:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{a}{t}\\ t_2 := x - y \cdot a\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+83}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-263}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 10^{-259}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 175:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ a t)))) (t_2 (- x (* y a))))
   (if (<= z -2.05e+83)
     (- x a)
     (if (<= z -1.55e-25)
       (+ x (/ (* y a) z))
       (if (<= z -3.5e-118)
         t_1
         (if (<= z -1.52e-263)
           t_2
           (if (<= z 1e-259)
             t_1
             (if (<= z 3e-78) t_2 (if (<= z 175.0) t_1 (- x a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (a / t));
	double t_2 = x - (y * a);
	double tmp;
	if (z <= -2.05e+83) {
		tmp = x - a;
	} else if (z <= -1.55e-25) {
		tmp = x + ((y * a) / z);
	} else if (z <= -3.5e-118) {
		tmp = t_1;
	} else if (z <= -1.52e-263) {
		tmp = t_2;
	} else if (z <= 1e-259) {
		tmp = t_1;
	} else if (z <= 3e-78) {
		tmp = t_2;
	} else if (z <= 175.0) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * (a / t))
    t_2 = x - (y * a)
    if (z <= (-2.05d+83)) then
        tmp = x - a
    else if (z <= (-1.55d-25)) then
        tmp = x + ((y * a) / z)
    else if (z <= (-3.5d-118)) then
        tmp = t_1
    else if (z <= (-1.52d-263)) then
        tmp = t_2
    else if (z <= 1d-259) then
        tmp = t_1
    else if (z <= 3d-78) then
        tmp = t_2
    else if (z <= 175.0d0) then
        tmp = t_1
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (a / t));
	double t_2 = x - (y * a);
	double tmp;
	if (z <= -2.05e+83) {
		tmp = x - a;
	} else if (z <= -1.55e-25) {
		tmp = x + ((y * a) / z);
	} else if (z <= -3.5e-118) {
		tmp = t_1;
	} else if (z <= -1.52e-263) {
		tmp = t_2;
	} else if (z <= 1e-259) {
		tmp = t_1;
	} else if (z <= 3e-78) {
		tmp = t_2;
	} else if (z <= 175.0) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (a / t))
	t_2 = x - (y * a)
	tmp = 0
	if z <= -2.05e+83:
		tmp = x - a
	elif z <= -1.55e-25:
		tmp = x + ((y * a) / z)
	elif z <= -3.5e-118:
		tmp = t_1
	elif z <= -1.52e-263:
		tmp = t_2
	elif z <= 1e-259:
		tmp = t_1
	elif z <= 3e-78:
		tmp = t_2
	elif z <= 175.0:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(a / t)))
	t_2 = Float64(x - Float64(y * a))
	tmp = 0.0
	if (z <= -2.05e+83)
		tmp = Float64(x - a);
	elseif (z <= -1.55e-25)
		tmp = Float64(x + Float64(Float64(y * a) / z));
	elseif (z <= -3.5e-118)
		tmp = t_1;
	elseif (z <= -1.52e-263)
		tmp = t_2;
	elseif (z <= 1e-259)
		tmp = t_1;
	elseif (z <= 3e-78)
		tmp = t_2;
	elseif (z <= 175.0)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (a / t));
	t_2 = x - (y * a);
	tmp = 0.0;
	if (z <= -2.05e+83)
		tmp = x - a;
	elseif (z <= -1.55e-25)
		tmp = x + ((y * a) / z);
	elseif (z <= -3.5e-118)
		tmp = t_1;
	elseif (z <= -1.52e-263)
		tmp = t_2;
	elseif (z <= 1e-259)
		tmp = t_1;
	elseif (z <= 3e-78)
		tmp = t_2;
	elseif (z <= 175.0)
		tmp = t_1;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+83], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.55e-25], N[(x + N[(N[(y * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-118], t$95$1, If[LessEqual[z, -1.52e-263], t$95$2, If[LessEqual[z, 1e-259], t$95$1, If[LessEqual[z, 3e-78], t$95$2, If[LessEqual[z, 175.0], t$95$1, N[(x - a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.05e83 or 175 < 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 79.0%

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

   if -2.05e83 < z < -1.54999999999999997e-25

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. distribute-neg-frac2 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in y around inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-/l* 68.0%

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

      3. distribute-rgt-neg-in 68.0%

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

   8. Simplified 68.0%

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

      1. sub-neg 68.0%

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

      2. distribute-rgt-neg-out 68.0%

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

      3. remove-double-neg 68.0%

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

      4. div-inv 68.0%

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

      5. associate-*r* 68.0%

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

      6. add-sqr-sqrt 31.0%

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

      7. sqrt-unprod 49.3%

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

      8. sqr-neg 49.3%

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

      9. sqrt-unprod 33.3%

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

      10. add-sqr-sqrt 42.8%

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

      11. div-inv 42.8%

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

      12. add-sqr-sqrt 33.3%

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

      13. sqrt-unprod 49.3%

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

      14. sqr-neg 49.3%

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

      15. sqrt-unprod 31.0%

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

      16. add-sqr-sqrt 68.1%

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

      17. *-commutative 68.1%

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

   10. Applied egg-rr 68.1%

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

   if -1.54999999999999997e-25 < z < -3.5e-118 or -1.52000000000000005e-263 < z < 1.0000000000000001e-259 or 2.99999999999999988e-78 < z < 175

   1. Initial program 99.9%

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

      1. associate-/r/ 99.8%

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

   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 86.7%

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

   6. Taylor expanded in y around inf 83.2%

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

      1. *-commutative 83.2%

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

      2. clear-num 83.1%

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

      3. un-div-inv 83.1%

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

   8. Applied egg-rr 83.1%

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

      1. associate-/r/ 83.2%

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

   10. Simplified 83.2%

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

   if -3.5e-118 < z < -1.52000000000000005e-263 or 1.0000000000000001e-259 < z < 2.99999999999999988e-78

   1. Initial program 98.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 94.4%

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

      1. *-commutative 94.4%

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

      2. associate-/l* 95.8%

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

   7. Simplified 95.8%

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

   8. Taylor expanded in t around 0 88.7%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+83}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y \cdot a}{z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-118}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-263}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 10^{-259}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-78}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 175:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+27} \lor \neg \left(t \leq 6 \cdot 10^{+89}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4e+27) (not (<= t 6e+89)))
   (+ x (* a (/ (- z y) t)))
   (- x (* a (/ (- y z) (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e+27) || !(t <= 6e+89)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4d+27)) .or. (.not. (t <= 6d+89))) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = x - (a * ((y - z) / (1.0d0 - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e+27) || !(t <= 6e+89)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4e+27) or not (t <= 6e+89):
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x - (a * ((y - z) / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4e+27) || !(t <= 6e+89))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4e+27) || ~((t <= 6e+89)))
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x - (a * ((y - z) / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4e+27], N[Not[LessEqual[t, 6e+89]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.0000000000000001e27 or 6.00000000000000025e89 < t

   1. Initial program 95.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 93.1%

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

   if -4.0000000000000001e27 < t < 6.00000000000000025e89

   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 98.5%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+27} \lor \neg \left(t \leq 6 \cdot 10^{+89}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+70} \lor \neg \left(z \leq 2.9 \cdot 10^{+155}\right):\\ \;\;\;\;x - \left(a - y \cdot \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 + \left(z - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+70) (not (<= z 2.9e+155)))
   (- x (- a (* y (/ a z))))
   (+ x (* y (/ a (+ -1.0 (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+70) || !(z <= 2.9e+155)) {
		tmp = x - (a - (y * (a / z)));
	} else {
		tmp = x + (y * (a / (-1.0 + (z - 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 <= (-4d+70)) .or. (.not. (z <= 2.9d+155))) then
        tmp = x - (a - (y * (a / z)))
    else
        tmp = x + (y * (a / ((-1.0d0) + (z - 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 <= -4e+70) || !(z <= 2.9e+155)) {
		tmp = x - (a - (y * (a / z)));
	} else {
		tmp = x + (y * (a / (-1.0 + (z - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e+70) or not (z <= 2.9e+155):
		tmp = x - (a - (y * (a / z)))
	else:
		tmp = x + (y * (a / (-1.0 + (z - t))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+70) || !(z <= 2.9e+155))
		tmp = Float64(x - Float64(a - Float64(y * Float64(a / z))));
	else
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 + Float64(z - t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4e+70) || ~((z <= 2.9e+155)))
		tmp = x - (a - (y * (a / z)));
	else
		tmp = x + (y * (a / (-1.0 + (z - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+70], N[Not[LessEqual[z, 2.9e+155]], $MachinePrecision]], N[(x - N[(a - N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(a / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.00000000000000029e70 or 2.8999999999999999e155 < z

   1. Initial program 90.7%

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

   3. Taylor expanded in z around inf 86.1%

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

      1. mul-1-neg 86.1%

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

      2. distribute-neg-frac2 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in y around 0 81.9%

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

      1. mul-1-neg 81.9%

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

      2. *-commutative 81.9%

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

      3. associate-*r/ 89.8%

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

      4. unsub-neg 89.8%

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

   8. Simplified 89.8%

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

   if -4.00000000000000029e70 < z < 2.8999999999999999e155

   1. Initial program 99.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 85.7%

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

      1. *-commutative 85.7%

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

      2. associate--l+ 85.7%

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

      3. +-commutative 85.7%

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

      4. associate-*r/ 92.2%

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

      5. +-commutative 92.2%

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

      6. associate--l+ 92.2%

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

      7. associate--l+ 92.2%

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

   7. Simplified 92.2%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+70} \lor \neg \left(z \leq 2.9 \cdot 10^{+155}\right):\\ \;\;\;\;x - \left(a - y \cdot \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 + \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+72}:\\ \;\;\;\;x - \left(a - y \cdot \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+89}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 + \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{z + \left(-1 - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+72)
   (- x (- a (* y (/ a z))))
   (if (<= z 4e+89)
     (+ x (* y (/ a (+ -1.0 (- z t)))))
     (- x (* a (/ z (+ z (- -1.0 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+72) {
		tmp = x - (a - (y * (a / z)));
	} else if (z <= 4e+89) {
		tmp = x + (y * (a / (-1.0 + (z - t))));
	} else {
		tmp = x - (a * (z / (z + (-1.0 - t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.3d+72)) then
        tmp = x - (a - (y * (a / z)))
    else if (z <= 4d+89) then
        tmp = x + (y * (a / ((-1.0d0) + (z - t))))
    else
        tmp = x - (a * (z / (z + ((-1.0d0) - t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+72) {
		tmp = x - (a - (y * (a / z)));
	} else if (z <= 4e+89) {
		tmp = x + (y * (a / (-1.0 + (z - t))));
	} else {
		tmp = x - (a * (z / (z + (-1.0 - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+72:
		tmp = x - (a - (y * (a / z)))
	elif z <= 4e+89:
		tmp = x + (y * (a / (-1.0 + (z - t))))
	else:
		tmp = x - (a * (z / (z + (-1.0 - t))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+72)
		tmp = Float64(x - Float64(a - Float64(y * Float64(a / z))));
	elseif (z <= 4e+89)
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 + Float64(z - t)))));
	else
		tmp = Float64(x - Float64(a * Float64(z / Float64(z + Float64(-1.0 - t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.3e+72)
		tmp = x - (a - (y * (a / z)));
	elseif (z <= 4e+89)
		tmp = x + (y * (a / (-1.0 + (z - t))));
	else
		tmp = x - (a * (z / (z + (-1.0 - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+72], N[(x - N[(a - N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+89], N[(x + N[(y * N[(a / N[(-1.0 + N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(z / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e72

   1. Initial program 90.2%

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

   3. Taylor expanded in z around inf 86.3%

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

      1. mul-1-neg 86.3%

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

      2. distribute-neg-frac2 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around 0 84.7%

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

      1. mul-1-neg 84.7%

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

      2. *-commutative 84.7%

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

      3. associate-*r/ 92.4%

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

      4. unsub-neg 92.4%

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

   8. Simplified 92.4%

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

   if -2.3e72 < z < 3.99999999999999998e89

   1. Initial program 99.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 86.8%

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

      1. *-commutative 86.8%

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

      2. associate--l+ 86.8%

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

      3. +-commutative 86.8%

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

      4. associate-*r/ 93.8%

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

      5. +-commutative 93.8%

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

      6. associate--l+ 93.8%

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

      7. associate--l+ 93.8%

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

   7. Simplified 93.8%

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

   if 3.99999999999999998e89 < z

   1. Initial program 94.2%

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

      1. associate-/r/ 99.9%

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

   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 90.4%

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

      1. mul-1-neg 90.4%

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

      2. associate--l+ 90.4%

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

      3. +-commutative 90.4%

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

      4. distribute-neg-frac2 90.4%

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

      5. +-commutative 90.4%

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

      6. distribute-neg-in 90.4%

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

      7. metadata-eval 90.4%

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

      8. unsub-neg 90.4%

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

      9. associate--r- 90.4%

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

   7. Simplified 90.4%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+72}:\\ \;\;\;\;x - \left(a - y \cdot \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+89}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 + \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{z + \left(-1 - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+18} \lor \neg \left(z \leq 7.8\right):\\ \;\;\;\;x - \left(a - y \cdot \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e+18) (not (<= z 7.8)))
   (- x (- a (* y (/ a z))))
   (- x (* y (/ a (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+18) || !(z <= 7.8)) {
		tmp = x - (a - (y * (a / z)));
	} else {
		tmp = x - (y * (a / (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 <= (-1.1d+18)) .or. (.not. (z <= 7.8d0))) then
        tmp = x - (a - (y * (a / z)))
    else
        tmp = x - (y * (a / (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 <= -1.1e+18) || !(z <= 7.8)) {
		tmp = x - (a - (y * (a / z)));
	} else {
		tmp = x - (y * (a / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e+18) or not (z <= 7.8):
		tmp = x - (a - (y * (a / z)))
	else:
		tmp = x - (y * (a / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e+18) || !(z <= 7.8))
		tmp = Float64(x - Float64(a - Float64(y * Float64(a / z))));
	else
		tmp = Float64(x - Float64(y * Float64(a / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.1e+18) || ~((z <= 7.8)))
		tmp = x - (a - (y * (a / z)));
	else
		tmp = x - (y * (a / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.1e+18], N[Not[LessEqual[z, 7.8]], $MachinePrecision]], N[(x - N[(a - N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e18 or 7.79999999999999982 < z

   1. Initial program 93.8%

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

   3. Taylor expanded in z around inf 83.2%

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

      1. mul-1-neg 83.2%

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

      2. distribute-neg-frac2 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in y around 0 78.9%

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

      1. mul-1-neg 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r/ 85.6%

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

      4. unsub-neg 85.6%

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

   8. Simplified 85.6%

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

   if -1.1e18 < z < 7.79999999999999982

   1. Initial program 99.2%

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

      1. associate-/r/ 99.9%

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

   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 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-/l* 94.9%

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

   7. Simplified 94.9%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+18} \lor \neg \left(z \leq 7.8\right):\\ \;\;\;\;x - \left(a - y \cdot \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+84} \lor \neg \left(z \leq 210\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.6e+84) (not (<= z 210.0)))
   (- x a)
   (- x (* y (/ a (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.6e+84) || !(z <= 210.0)) {
		tmp = x - a;
	} else {
		tmp = x - (y * (a / (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 <= (-3.6d+84)) .or. (.not. (z <= 210.0d0))) then
        tmp = x - a
    else
        tmp = x - (y * (a / (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 <= -3.6e+84) || !(z <= 210.0)) {
		tmp = x - a;
	} else {
		tmp = x - (y * (a / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.6e+84) or not (z <= 210.0):
		tmp = x - a
	else:
		tmp = x - (y * (a / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.6e+84) || !(z <= 210.0))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * Float64(a / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.6e+84) || ~((z <= 210.0)))
		tmp = x - a;
	else
		tmp = x - (y * (a / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.6e+84], N[Not[LessEqual[z, 210.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5999999999999999e84 or 210 < 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 79.0%

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

   if -3.5999999999999999e84 < z < 210

   1. Initial program 99.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 83.9%

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

      1. *-commutative 83.9%

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

      2. associate-/l* 91.1%

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

   7. Simplified 91.1%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+84} \lor \neg \left(z \leq 210\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+82} \lor \neg \left(z \leq 3.6 \cdot 10^{-11}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e+82) (not (<= z 3.6e-11))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+82) || !(z <= 3.6e-11)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.6d+82)) .or. (.not. (z <= 3.6d-11))) then
        tmp = x - a
    else
        tmp = x - (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+82) || !(z <= 3.6e-11)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.6e+82) or not (z <= 3.6e-11):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.6e+82) || !(z <= 3.6e-11))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.6e+82) || ~((z <= 3.6e-11)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.6e+82], N[Not[LessEqual[z, 3.6e-11]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999987e82 or 3.59999999999999985e-11 < z

   1. Initial program 92.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 78.7%

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

   if -1.59999999999999987e82 < z < 3.59999999999999985e-11

   1. Initial program 99.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 0 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-/l* 91.0%

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

   7. Simplified 91.0%

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

   8. Taylor expanded in t around 0 72.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+82} \lor \neg \left(z \leq 3.6 \cdot 10^{-11}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+15} \lor \neg \left(z \leq 1600000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.05e+15) (not (<= z 1600000000.0))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.05e+15) || !(z <= 1600000000.0)) {
		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 <= (-2.05d+15)) .or. (.not. (z <= 1600000000.0d0))) 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 <= -2.05e+15) || !(z <= 1600000000.0)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.05e+15) or not (z <= 1600000000.0):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.05e+15) || !(z <= 1600000000.0))
		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 <= -2.05e+15) || ~((z <= 1600000000.0)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.05e+15], N[Not[LessEqual[z, 1600000000.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.05e15 or 1.6e9 < z

   1. Initial program 93.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 73.7%

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

   if -2.05e15 < z < 1.6e9

   1. Initial program 99.2%

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

      1. associate-/r/ 99.9%

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

   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 inf 87.6%

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

      1. *-commutative 87.6%

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

      2. associate--l+ 87.6%

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

      3. +-commutative 87.6%

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

      4. associate-*r/ 95.1%

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

      5. +-commutative 95.1%

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

      6. associate--l+ 95.1%

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

      7. associate--l+ 95.1%

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

   7. Simplified 95.1%

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

   8. Taylor expanded in x around inf 55.8%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+15} \lor \neg \left(z \leq 1600000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.1% 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 96.5%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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 y around inf 75.4%

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

   1. *-commutative 75.4%

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

   2. associate--l+ 75.4%

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

   3. +-commutative 75.4%

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

   4. associate-*r/ 80.9%

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

   5. +-commutative 80.9%

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

   6. associate--l+ 80.9%

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

   7. associate--l+ 80.9%

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

7. Simplified 80.9%

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

8. Taylor expanded in x around inf 52.6%

   \[\leadsto \color{blue}{x} \]
9. 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 2024086 
(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))))