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

Percentage Accurate: 96.9% → 99.7%

Time: 10.6s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-/r/ 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 67.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+51}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 0.00016:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+59} \lor \neg \left(z \leq 2.65 \cdot 10^{+97}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.1e+51)
   (- x a)
   (if (<= z 0.00016)
     (- x (/ (* y a) t))
     (if (or (<= z 2.7e+59) (not (<= z 2.65e+97)))
       (- x a)
       (* a (/ y (+ z (- -1.0 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e+51) {
		tmp = x - a;
	} else if (z <= 0.00016) {
		tmp = x - ((y * a) / t);
	} else if ((z <= 2.7e+59) || !(z <= 2.65e+97)) {
		tmp = x - a;
	} else {
		tmp = a * (y / (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 <= (-3.1d+51)) then
        tmp = x - a
    else if (z <= 0.00016d0) then
        tmp = x - ((y * a) / t)
    else if ((z <= 2.7d+59) .or. (.not. (z <= 2.65d+97))) then
        tmp = x - a
    else
        tmp = a * (y / (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 <= -3.1e+51) {
		tmp = x - a;
	} else if (z <= 0.00016) {
		tmp = x - ((y * a) / t);
	} else if ((z <= 2.7e+59) || !(z <= 2.65e+97)) {
		tmp = x - a;
	} else {
		tmp = a * (y / (z + (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.1e+51:
		tmp = x - a
	elif z <= 0.00016:
		tmp = x - ((y * a) / t)
	elif (z <= 2.7e+59) or not (z <= 2.65e+97):
		tmp = x - a
	else:
		tmp = a * (y / (z + (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.1e+51)
		tmp = Float64(x - a);
	elseif (z <= 0.00016)
		tmp = Float64(x - Float64(Float64(y * a) / t));
	elseif ((z <= 2.7e+59) || !(z <= 2.65e+97))
		tmp = Float64(x - a);
	else
		tmp = Float64(a * Float64(y / 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 <= -3.1e+51)
		tmp = x - a;
	elseif (z <= 0.00016)
		tmp = x - ((y * a) / t);
	elseif ((z <= 2.7e+59) || ~((z <= 2.65e+97)))
		tmp = x - a;
	else
		tmp = a * (y / (z + (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.1e+51], N[(x - a), $MachinePrecision], If[LessEqual[z, 0.00016], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.7e+59], N[Not[LessEqual[z, 2.65e+97]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(a * N[(y / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.10000000000000011e51 or 1.60000000000000013e-4 < z < 2.7000000000000001e59 or 2.6500000000000001e97 < z

   1. Initial program 94.5%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 75.7%

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

   if -3.10000000000000011e51 < z < 1.60000000000000013e-4

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 69.7%

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

   4. Taylor expanded in y around inf 65.7%

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

   if 2.7000000000000001e59 < z < 2.6500000000000001e97

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-/r/ 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. associate-*l/ 99.7%

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

      6. associate-/l* 99.5%

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

      7. fma-define 99.5%

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

      8. distribute-frac-neg 99.5%

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

      9. distribute-neg-frac2 99.5%

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

      10. distribute-neg-in 99.5%

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

      11. sub-neg 99.5%

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

      12. distribute-neg-in 99.5%

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

      13. remove-double-neg 99.5%

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

      14. +-commutative 99.5%

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

      15. sub-neg 99.5%

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

      16. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 89.3%

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

      1. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+51}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 0.00016:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+59} \lor \neg \left(z \leq 2.65 \cdot 10^{+97}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+52}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+21}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+59} \lor \neg \left(z \leq 2.65 \cdot 10^{+97}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y}{z - \left(t + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.6e+52)
   (- x a)
   (if (<= z 1.4e+21)
     (+ x (* z (/ a (+ t 1.0))))
     (if (or (<= z 2e+59) (not (<= z 2.65e+97)))
       (- x a)
       (* a (/ y (- z (+ t 1.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.6e+52) {
		tmp = x - a;
	} else if (z <= 1.4e+21) {
		tmp = x + (z * (a / (t + 1.0)));
	} else if ((z <= 2e+59) || !(z <= 2.65e+97)) {
		tmp = x - a;
	} else {
		tmp = a * (y / (z - (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 <= (-4.6d+52)) then
        tmp = x - a
    else if (z <= 1.4d+21) then
        tmp = x + (z * (a / (t + 1.0d0)))
    else if ((z <= 2d+59) .or. (.not. (z <= 2.65d+97))) then
        tmp = x - a
    else
        tmp = a * (y / (z - (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 <= -4.6e+52) {
		tmp = x - a;
	} else if (z <= 1.4e+21) {
		tmp = x + (z * (a / (t + 1.0)));
	} else if ((z <= 2e+59) || !(z <= 2.65e+97)) {
		tmp = x - a;
	} else {
		tmp = a * (y / (z - (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.6e+52:
		tmp = x - a
	elif z <= 1.4e+21:
		tmp = x + (z * (a / (t + 1.0)))
	elif (z <= 2e+59) or not (z <= 2.65e+97):
		tmp = x - a
	else:
		tmp = a * (y / (z - (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.6e+52)
		tmp = Float64(x - a);
	elseif (z <= 1.4e+21)
		tmp = Float64(x + Float64(z * Float64(a / Float64(t + 1.0))));
	elseif ((z <= 2e+59) || !(z <= 2.65e+97))
		tmp = Float64(x - a);
	else
		tmp = Float64(a * Float64(y / Float64(z - Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.6e+52)
		tmp = x - a;
	elseif (z <= 1.4e+21)
		tmp = x + (z * (a / (t + 1.0)));
	elseif ((z <= 2e+59) || ~((z <= 2.65e+97)))
		tmp = x - a;
	else
		tmp = a * (y / (z - (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.6e+52], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.4e+21], N[(x + N[(z * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2e+59], N[Not[LessEqual[z, 2.65e+97]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(a * N[(y / N[(z - N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e52 or 1.4e21 < z < 1.99999999999999994e59 or 2.6500000000000001e97 < z

   1. Initial program 94.1%

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

      1. associate-/r/ 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 79.1%

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

   if -4.6e52 < z < 1.4e21

   1. Initial program 99.8%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0 68.1%

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

      1. associate-*r/ 68.1%

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

      2. mul-1-neg 68.1%

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

      3. associate--l+ 68.1%

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

      4. distribute-neg-in 68.1%

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

      5. metadata-eval 68.1%

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

      6. unsub-neg 68.1%

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

   9. Simplified 68.1%

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

   10. Taylor expanded in z around 0 65.7%

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

       1. mul-1-neg 65.7%

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

       2. *-commutative 65.7%

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

       3. associate-/l* 67.6%

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

       4. distribute-rgt-neg-out 67.6%

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

       5. distribute-neg-frac2 67.6%

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

       6. distribute-neg-in 67.6%

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

       7. metadata-eval 67.6%

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

       8. sub-neg 67.6%

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

   12. Simplified 67.6%

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

   if 1.99999999999999994e59 < z < 2.6500000000000001e97

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-/r/ 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. associate-*l/ 99.7%

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

      6. associate-/l* 99.5%

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

      7. fma-define 99.5%

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

      8. distribute-frac-neg 99.5%

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

      9. distribute-neg-frac2 99.5%

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

      10. distribute-neg-in 99.5%

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

      11. sub-neg 99.5%

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

      12. distribute-neg-in 99.5%

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

      13. remove-double-neg 99.5%

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

      14. +-commutative 99.5%

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

      15. sub-neg 99.5%

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

      16. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 89.3%

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

      1. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+52}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+21}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+59} \lor \neg \left(z \leq 2.65 \cdot 10^{+97}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y}{z - \left(t + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -68000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{-209}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-160}:\\ \;\;\;\;a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+14}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ (- y z) t)))))
   (if (<= t -68000000000000.0)
     t_1
     (if (<= t 1.66e-209)
       (- x a)
       (if (<= t 5.3e-160)
         (* a (/ y (- -1.0 t)))
         (if (<= t 3e+14) (- x a) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * ((y - z) / t));
	double tmp;
	if (t <= -68000000000000.0) {
		tmp = t_1;
	} else if (t <= 1.66e-209) {
		tmp = x - a;
	} else if (t <= 5.3e-160) {
		tmp = a * (y / (-1.0 - t));
	} else if (t <= 3e+14) {
		tmp = x - a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (a * ((y - z) / t))
    if (t <= (-68000000000000.0d0)) then
        tmp = t_1
    else if (t <= 1.66d-209) then
        tmp = x - a
    else if (t <= 5.3d-160) then
        tmp = a * (y / ((-1.0d0) - t))
    else if (t <= 3d+14) then
        tmp = x - a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * ((y - z) / t));
	double tmp;
	if (t <= -68000000000000.0) {
		tmp = t_1;
	} else if (t <= 1.66e-209) {
		tmp = x - a;
	} else if (t <= 5.3e-160) {
		tmp = a * (y / (-1.0 - t));
	} else if (t <= 3e+14) {
		tmp = x - a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * ((y - z) / t))
	tmp = 0
	if t <= -68000000000000.0:
		tmp = t_1
	elif t <= 1.66e-209:
		tmp = x - a
	elif t <= 5.3e-160:
		tmp = a * (y / (-1.0 - t))
	elif t <= 3e+14:
		tmp = x - a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(Float64(y - z) / t)))
	tmp = 0.0
	if (t <= -68000000000000.0)
		tmp = t_1;
	elseif (t <= 1.66e-209)
		tmp = Float64(x - a);
	elseif (t <= 5.3e-160)
		tmp = Float64(a * Float64(y / Float64(-1.0 - t)));
	elseif (t <= 3e+14)
		tmp = Float64(x - a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * ((y - z) / t));
	tmp = 0.0;
	if (t <= -68000000000000.0)
		tmp = t_1;
	elseif (t <= 1.66e-209)
		tmp = x - a;
	elseif (t <= 5.3e-160)
		tmp = a * (y / (-1.0 - t));
	elseif (t <= 3e+14)
		tmp = x - a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -68000000000000.0], t$95$1, If[LessEqual[t, 1.66e-209], N[(x - a), $MachinePrecision], If[LessEqual[t, 5.3e-160], N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+14], N[(x - a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.8e13 or 3e14 < t

   1. Initial program 96.6%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 86.5%

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

   if -6.8e13 < t < 1.66e-209 or 5.3000000000000001e-160 < t < 3e14

   1. Initial program 98.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 63.7%

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

   if 1.66e-209 < t < 5.3000000000000001e-160

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-/r/ 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. associate-*l/ 100.0%

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

      6. associate-/l* 100.0%

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

      7. fma-define 100.0%

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

      8. distribute-frac-neg 100.0%

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

      9. distribute-neg-frac2 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. sub-neg 100.0%

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

      12. distribute-neg-in 100.0%

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

      13. remove-double-neg 100.0%

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

      14. +-commutative 100.0%

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

      15. sub-neg 100.0%

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

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 75.8%

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

      1. associate-/l* 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in z around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. associate-/l* 75.8%

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

      3. distribute-rgt-neg-in 75.8%

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

      4. distribute-neg-frac2 75.8%

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

      5. distribute-neg-in 75.8%

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

      6. metadata-eval 75.8%

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

      7. unsub-neg 75.8%

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

   10. Simplified 75.8%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -68000000000000:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{-209}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-160}:\\ \;\;\;\;a \cdot \frac{y}{-1 - t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+14}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - y}{\frac{t}{a}}\\ t_2 := x - \left(a - a \cdot \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-114}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z y) (/ t a)))) (t_2 (- x (- a (* a (/ y z))))))
   (if (<= z -1.8e+51)
     t_2
     (if (<= z -9.6e-293)
       t_1
       (if (<= z 3.2e-114)
         (+ x (* z (/ a (+ t 1.0))))
         (if (<= z 1e+21) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) / (t / a));
	double t_2 = x - (a - (a * (y / z)));
	double tmp;
	if (z <= -1.8e+51) {
		tmp = t_2;
	} else if (z <= -9.6e-293) {
		tmp = t_1;
	} else if (z <= 3.2e-114) {
		tmp = x + (z * (a / (t + 1.0)));
	} else if (z <= 1e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z - y) / (t / a))
    t_2 = x - (a - (a * (y / z)))
    if (z <= (-1.8d+51)) then
        tmp = t_2
    else if (z <= (-9.6d-293)) then
        tmp = t_1
    else if (z <= 3.2d-114) then
        tmp = x + (z * (a / (t + 1.0d0)))
    else if (z <= 1d+21) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) / (t / a));
	double t_2 = x - (a - (a * (y / z)));
	double tmp;
	if (z <= -1.8e+51) {
		tmp = t_2;
	} else if (z <= -9.6e-293) {
		tmp = t_1;
	} else if (z <= 3.2e-114) {
		tmp = x + (z * (a / (t + 1.0)));
	} else if (z <= 1e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) / (t / a))
	t_2 = x - (a - (a * (y / z)))
	tmp = 0
	if z <= -1.8e+51:
		tmp = t_2
	elif z <= -9.6e-293:
		tmp = t_1
	elif z <= 3.2e-114:
		tmp = x + (z * (a / (t + 1.0)))
	elif z <= 1e+21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) / Float64(t / a)))
	t_2 = Float64(x - Float64(a - Float64(a * Float64(y / z))))
	tmp = 0.0
	if (z <= -1.8e+51)
		tmp = t_2;
	elseif (z <= -9.6e-293)
		tmp = t_1;
	elseif (z <= 3.2e-114)
		tmp = Float64(x + Float64(z * Float64(a / Float64(t + 1.0))));
	elseif (z <= 1e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) / (t / a));
	t_2 = x - (a - (a * (y / z)));
	tmp = 0.0;
	if (z <= -1.8e+51)
		tmp = t_2;
	elseif (z <= -9.6e-293)
		tmp = t_1;
	elseif (z <= 3.2e-114)
		tmp = x + (z * (a / (t + 1.0)));
	elseif (z <= 1e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a - N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+51], t$95$2, If[LessEqual[z, -9.6e-293], t$95$1, If[LessEqual[z, 3.2e-114], N[(x + N[(z * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+21], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.80000000000000005e51 or 1e21 < z

   1. Initial program 94.5%

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

   3. Taylor expanded in z around inf 80.6%

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

      1. mul-1-neg 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in y around 0 80.8%

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

      1. mul-1-neg 80.8%

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

      2. unsub-neg 80.8%

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

      3. associate-/l* 84.3%

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

   8. Simplified 84.3%

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

   if -1.80000000000000005e51 < z < -9.5999999999999996e-293 or 3.2000000000000002e-114 < z < 1e21

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 74.8%

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

   if -9.5999999999999996e-293 < z < 3.2000000000000002e-114

   1. Initial program 99.8%

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

      1. *-commutative 100.0%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 69.6%

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

      1. associate-*r/ 69.6%

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

      2. mul-1-neg 69.6%

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

      3. associate--l+ 69.6%

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

      4. distribute-neg-in 69.6%

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

      5. metadata-eval 69.6%

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

      6. unsub-neg 69.6%

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

   9. Simplified 69.6%

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

   10. Taylor expanded in z around 0 69.6%

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

       1. mul-1-neg 69.6%

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

       2. *-commutative 69.6%

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

       3. associate-/l* 69.6%

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

       4. distribute-rgt-neg-out 69.6%

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

       5. distribute-neg-frac2 69.6%

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

       6. distribute-neg-in 69.6%

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

       7. metadata-eval 69.6%

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

       8. sub-neg 69.6%

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

   12. Simplified 69.6%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+51}:\\ \;\;\;\;x - \left(a - a \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-293}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-114}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{elif}\;z \leq 10^{+21}:\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(a - a \cdot \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{y - z}{-1 - \left(t - z\right)}\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+24}:\\ \;\;\;\;x - \frac{z \cdot a}{z + -1}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+135}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* a (/ (- y z) (- -1.0 (- t z))))))
   (if (<= a -8.8e+38)
     t_1
     (if (<= a 2.2e+24)
       (- x (/ (* z a) (+ z -1.0)))
       (if (<= a 1.35e+135) (+ x (* z (/ a (+ t 1.0)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a * ((y - z) / (-1.0 - (t - z)));
	double tmp;
	if (a <= -8.8e+38) {
		tmp = t_1;
	} else if (a <= 2.2e+24) {
		tmp = x - ((z * a) / (z + -1.0));
	} else if (a <= 1.35e+135) {
		tmp = x + (z * (a / (t + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((y - z) / ((-1.0d0) - (t - z)))
    if (a <= (-8.8d+38)) then
        tmp = t_1
    else if (a <= 2.2d+24) then
        tmp = x - ((z * a) / (z + (-1.0d0)))
    else if (a <= 1.35d+135) then
        tmp = x + (z * (a / (t + 1.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a * ((y - z) / (-1.0 - (t - z)));
	double tmp;
	if (a <= -8.8e+38) {
		tmp = t_1;
	} else if (a <= 2.2e+24) {
		tmp = x - ((z * a) / (z + -1.0));
	} else if (a <= 1.35e+135) {
		tmp = x + (z * (a / (t + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a * ((y - z) / (-1.0 - (t - z)))
	tmp = 0
	if a <= -8.8e+38:
		tmp = t_1
	elif a <= 2.2e+24:
		tmp = x - ((z * a) / (z + -1.0))
	elif a <= 1.35e+135:
		tmp = x + (z * (a / (t + 1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a * Float64(Float64(y - z) / Float64(-1.0 - Float64(t - z))))
	tmp = 0.0
	if (a <= -8.8e+38)
		tmp = t_1;
	elseif (a <= 2.2e+24)
		tmp = Float64(x - Float64(Float64(z * a) / Float64(z + -1.0)));
	elseif (a <= 1.35e+135)
		tmp = Float64(x + Float64(z * Float64(a / Float64(t + 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a * ((y - z) / (-1.0 - (t - z)));
	tmp = 0.0;
	if (a <= -8.8e+38)
		tmp = t_1;
	elseif (a <= 2.2e+24)
		tmp = x - ((z * a) / (z + -1.0));
	elseif (a <= 1.35e+135)
		tmp = x + (z * (a / (t + 1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * N[(N[(y - z), $MachinePrecision] / N[(-1.0 - N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.8e+38], t$95$1, If[LessEqual[a, 2.2e+24], N[(x - N[(N[(z * a), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+135], N[(x + N[(z * N[(a / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.80000000000000026e38 or 1.34999999999999992e135 < a

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-/r/ 99.6%

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

      4. distribute-rgt-neg-in 99.6%

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

      5. associate-*l/ 63.7%

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

      6. associate-/l* 99.8%

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

      7. fma-define 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. sub-neg 99.9%

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

      12. distribute-neg-in 99.9%

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

      13. remove-double-neg 99.9%

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

      14. +-commutative 99.9%

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

      15. sub-neg 99.9%

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

      16. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around inf 82.3%

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

      1. div-sub 82.3%

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

      2. +-commutative 82.3%

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

      3. metadata-eval 82.3%

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

      4. sub-neg 82.3%

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

      5. associate-+l- 82.3%

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

      6. +-commutative 82.3%

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

   7. Simplified 82.3%

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

   if -8.80000000000000026e38 < a < 2.20000000000000002e24

   1. Initial program 96.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 85.0%

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

      1. associate-*r/ 85.0%

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

      2. mul-1-neg 85.0%

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

      3. associate--l+ 85.0%

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

      4. distribute-neg-in 85.0%

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

      5. metadata-eval 85.0%

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

      6. unsub-neg 85.0%

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

   9. Simplified 85.0%

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

   10. Taylor expanded in t around 0 81.1%

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

   if 2.20000000000000002e24 < a < 1.34999999999999992e135

   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. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 85.5%

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

      1. associate-*r/ 85.5%

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

      2. mul-1-neg 85.5%

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

      3. associate--l+ 85.5%

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

      4. distribute-neg-in 85.5%

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

      5. metadata-eval 85.5%

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

      6. unsub-neg 85.5%

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

   9. Simplified 85.5%

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

   10. Taylor expanded in z around 0 66.6%

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

       1. mul-1-neg 66.6%

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

       2. *-commutative 66.6%

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

       3. associate-/l* 70.1%

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

       4. distribute-rgt-neg-out 70.1%

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

       5. distribute-neg-frac2 70.1%

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

       6. distribute-neg-in 70.1%

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

       7. metadata-eval 70.1%

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

       8. sub-neg 70.1%

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

   12. Simplified 70.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \frac{y - z}{-1 - \left(t - z\right)}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+24}:\\ \;\;\;\;x - \frac{z \cdot a}{z + -1}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+135}:\\ \;\;\;\;x + z \cdot \frac{a}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y - z}{-1 - \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 - \left(t - z\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+55} \lor \neg \left(a \leq 4.5 \cdot 10^{+166}\right):\\ \;\;\;\;a \cdot \frac{y - z}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t\_1}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- -1.0 (- t z))))
   (if (or (<= a -1.05e+55) (not (<= a 4.5e+166)))
     (* a (/ (- y z) t_1))
     (- x (/ a (/ t_1 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -1.0 - (t - z);
	double tmp;
	if ((a <= -1.05e+55) || !(a <= 4.5e+166)) {
		tmp = a * ((y - z) / t_1);
	} else {
		tmp = x - (a / (t_1 / 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) :: t_1
    real(8) :: tmp
    t_1 = (-1.0d0) - (t - z)
    if ((a <= (-1.05d+55)) .or. (.not. (a <= 4.5d+166))) then
        tmp = a * ((y - z) / t_1)
    else
        tmp = x - (a / (t_1 / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -1.0 - (t - z);
	double tmp;
	if ((a <= -1.05e+55) || !(a <= 4.5e+166)) {
		tmp = a * ((y - z) / t_1);
	} else {
		tmp = x - (a / (t_1 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -1.0 - (t - z)
	tmp = 0
	if (a <= -1.05e+55) or not (a <= 4.5e+166):
		tmp = a * ((y - z) / t_1)
	else:
		tmp = x - (a / (t_1 / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-1.0 - Float64(t - z))
	tmp = 0.0
	if ((a <= -1.05e+55) || !(a <= 4.5e+166))
		tmp = Float64(a * Float64(Float64(y - z) / t_1));
	else
		tmp = Float64(x - Float64(a / Float64(t_1 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -1.0 - (t - z);
	tmp = 0.0;
	if ((a <= -1.05e+55) || ~((a <= 4.5e+166)))
		tmp = a * ((y - z) / t_1);
	else
		tmp = x - (a / (t_1 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-1.0 - N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -1.05e+55], N[Not[LessEqual[a, 4.5e+166]], $MachinePrecision]], N[(a * N[(N[(y - z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.05e55 or 4.5000000000000003e166 < a

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-/r/ 99.6%

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

      4. distribute-rgt-neg-in 99.6%

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

      5. associate-*l/ 63.7%

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

      6. associate-/l* 99.9%

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

      7. fma-define 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. sub-neg 99.9%

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

      12. distribute-neg-in 99.9%

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

      13. remove-double-neg 99.9%

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

      14. +-commutative 99.9%

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

      15. sub-neg 99.9%

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

      16. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around inf 84.2%

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

      1. div-sub 84.2%

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

      2. +-commutative 84.2%

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

      3. metadata-eval 84.2%

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

      4. sub-neg 84.2%

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

      5. associate-+l- 84.2%

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

      6. +-commutative 84.2%

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

   7. Simplified 84.2%

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

   if -1.05e55 < a < 4.5000000000000003e166

   1. Initial program 96.8%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 84.6%

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

      1. associate-*r/ 84.6%

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

      2. mul-1-neg 84.6%

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

      3. associate--l+ 84.6%

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

      4. distribute-neg-in 84.6%

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

      5. metadata-eval 84.6%

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

      6. unsub-neg 84.6%

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

   9. Simplified 84.6%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+55} \lor \neg \left(a \leq 4.5 \cdot 10^{+166}\right):\\ \;\;\;\;a \cdot \frac{y - z}{-1 - \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{-1 - \left(t - z\right)}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+51} \lor \neg \left(z \leq 1.35 \cdot 10^{+21}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3e+51) (not (<= z 1.35e+21)))
   (+ x (- (* a (/ y z)) a))
   (- x (* a (/ (- y z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e+51) || !(z <= 1.35e+21)) {
		tmp = x + ((a * (y / z)) - a);
	} else {
		tmp = x - (a * ((y - 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 <= (-3d+51)) .or. (.not. (z <= 1.35d+21))) then
        tmp = x + ((a * (y / z)) - a)
    else
        tmp = x - (a * ((y - 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 <= -3e+51) || !(z <= 1.35e+21)) {
		tmp = x + ((a * (y / z)) - a);
	} else {
		tmp = x - (a * ((y - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3e+51) or not (z <= 1.35e+21):
		tmp = x + ((a * (y / z)) - a)
	else:
		tmp = x - (a * ((y - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3e+51) || !(z <= 1.35e+21))
		tmp = Float64(x + Float64(Float64(a * Float64(y / z)) - a));
	else
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3e+51) || ~((z <= 1.35e+21)))
		tmp = x + ((a * (y / z)) - a);
	else
		tmp = x - (a * ((y - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3e+51], N[Not[LessEqual[z, 1.35e+21]], $MachinePrecision]], N[(x + N[(N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e51 or 1.35e21 < z

   1. Initial program 94.5%

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

   3. Taylor expanded in z around inf 80.6%

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

      1. mul-1-neg 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in y around 0 80.8%

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

      1. mul-1-neg 80.8%

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

      2. unsub-neg 80.8%

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

      3. associate-/l* 84.3%

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

   8. Simplified 84.3%

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

   if -3e51 < z < 1.35e21

   1. Initial program 99.8%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 68.7%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+51} \lor \neg \left(z \leq 1.35 \cdot 10^{+21}\right):\\ \;\;\;\;x + \left(a \cdot \frac{y}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+51} \lor \neg \left(z \leq 1.35 \cdot 10^{+21}\right):\\ \;\;\;\;x - \left(a - a \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.8e+51) (not (<= z 1.35e+21)))
   (- x (- a (* a (/ y z))))
   (+ x (/ a (/ t (- z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.8e+51) || !(z <= 1.35e+21)) {
		tmp = x - (a - (a * (y / z)));
	} else {
		tmp = x + (a / (t / (z - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.8d+51)) .or. (.not. (z <= 1.35d+21))) then
        tmp = x - (a - (a * (y / z)))
    else
        tmp = x + (a / (t / (z - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.8e+51) || !(z <= 1.35e+21)) {
		tmp = x - (a - (a * (y / z)));
	} else {
		tmp = x + (a / (t / (z - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.8e+51) or not (z <= 1.35e+21):
		tmp = x - (a - (a * (y / z)))
	else:
		tmp = x + (a / (t / (z - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.8e+51) || !(z <= 1.35e+21))
		tmp = Float64(x - Float64(a - Float64(a * Float64(y / z))));
	else
		tmp = Float64(x + Float64(a / Float64(t / Float64(z - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.8e+51) || ~((z <= 1.35e+21)))
		tmp = x - (a - (a * (y / z)));
	else
		tmp = x + (a / (t / (z - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.8e+51], N[Not[LessEqual[z, 1.35e+21]], $MachinePrecision]], N[(x - N[(a - N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a / N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000005e51 or 1.35e21 < z

   1. Initial program 94.5%

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

   3. Taylor expanded in z around inf 80.6%

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

      1. mul-1-neg 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in y around 0 80.8%

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

      1. mul-1-neg 80.8%

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

      2. unsub-neg 80.8%

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

      3. associate-/l* 84.3%

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

   8. Simplified 84.3%

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

   if -1.80000000000000005e51 < z < 1.35e21

   1. Initial program 99.8%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in t around inf 69.3%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+51} \lor \neg \left(z \leq 1.35 \cdot 10^{+21}\right):\\ \;\;\;\;x - \left(a - a \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+51} \lor \neg \left(z \leq 0.00018\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e+51) (not (<= z 0.00018))) (- x a) (- x (/ (* y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+51) || !(z <= 0.00018)) {
		tmp = x - a;
	} else {
		tmp = x - ((y * a) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.6d+51)) .or. (.not. (z <= 0.00018d0))) then
        tmp = x - a
    else
        tmp = x - ((y * a) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+51) || !(z <= 0.00018)) {
		tmp = x - a;
	} else {
		tmp = x - ((y * a) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e+51) or not (z <= 0.00018):
		tmp = x - a
	else:
		tmp = x - ((y * a) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e+51) || !(z <= 0.00018))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(Float64(y * a) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.6e+51) || ~((z <= 0.00018)))
		tmp = x - a;
	else
		tmp = x - ((y * a) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e+51], N[Not[LessEqual[z, 0.00018]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6000000000000001e51 or 1.80000000000000011e-4 < z

   1. Initial program 94.8%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 72.1%

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

   if -2.6000000000000001e51 < z < 1.80000000000000011e-4

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 69.7%

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

   4. Taylor expanded in y around inf 65.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+51} \lor \neg \left(z \leq 0.00018\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+51} \lor \neg \left(z \leq 0.00018\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.8e+51) (not (<= z 0.00018))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.8e+51) || !(z <= 0.00018)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.8d+51)) .or. (.not. (z <= 0.00018d0))) then
        tmp = x - a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.8e+51) || !(z <= 0.00018)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.8e+51) or not (z <= 0.00018):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.8e+51) || !(z <= 0.00018))
		tmp = Float64(x - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.8e+51) || ~((z <= 0.00018)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.8e+51], N[Not[LessEqual[z, 0.00018]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000005e51 or 1.80000000000000011e-4 < z

   1. Initial program 94.8%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 72.1%

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

   if -1.80000000000000005e51 < z < 1.80000000000000011e-4

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-/r/ 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. associate-*l/ 95.5%

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

      6. associate-/l* 99.9%

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

      7. fma-define 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. sub-neg 99.9%

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

      12. distribute-neg-in 99.9%

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

      13. remove-double-neg 99.9%

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

      14. +-commutative 99.9%

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

      15. sub-neg 99.9%

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

      16. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 62.7%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+51} \lor \neg \left(z \leq 0.00018\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.8% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. sub-neg 97.6%

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

   2. +-commutative 97.6%

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

   3. associate-/r/ 99.8%

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

   4. distribute-rgt-neg-in 99.8%

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

   5. associate-*l/ 86.3%

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

   6. associate-/l* 98.5%

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

   7. fma-define 98.5%

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

   8. distribute-frac-neg 98.5%

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

   9. distribute-neg-frac2 98.5%

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

   10. distribute-neg-in 98.5%

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

   11. sub-neg 98.5%

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

   12. distribute-neg-in 98.5%

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

   13. remove-double-neg 98.5%

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

   14. +-commutative 98.5%

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

   15. sub-neg 98.5%

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

   16. metadata-eval 98.5%

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

3. Simplified 98.5%

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

5. Taylor expanded in a around 0 55.9%

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

6. Final simplification 55.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024095 
(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))))