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

Percentage Accurate: 96.8% → 99.6%

Time: 9.0s

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: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

   1. associate-/r/ 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{if}\;t \leq -3300000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-292}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-86}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-11}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ a t) (- z y)))))
   (if (<= t -3300000000.0)
     t_1
     (if (<= t -3.45e-292)
       (+ x (/ a (/ (- 1.0 z) z)))
       (if (<= t 5e-86) (- x (* y a)) (if (<= t 7e-11) (- x a) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((a / t) * (z - y));
	double tmp;
	if (t <= -3300000000.0) {
		tmp = t_1;
	} else if (t <= -3.45e-292) {
		tmp = x + (a / ((1.0 - z) / z));
	} else if (t <= 5e-86) {
		tmp = x - (y * a);
	} else if (t <= 7e-11) {
		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 / t) * (z - y))
    if (t <= (-3300000000.0d0)) then
        tmp = t_1
    else if (t <= (-3.45d-292)) then
        tmp = x + (a / ((1.0d0 - z) / z))
    else if (t <= 5d-86) then
        tmp = x - (y * a)
    else if (t <= 7d-11) 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 / t) * (z - y));
	double tmp;
	if (t <= -3300000000.0) {
		tmp = t_1;
	} else if (t <= -3.45e-292) {
		tmp = x + (a / ((1.0 - z) / z));
	} else if (t <= 5e-86) {
		tmp = x - (y * a);
	} else if (t <= 7e-11) {
		tmp = x - a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((a / t) * (z - y))
	tmp = 0
	if t <= -3300000000.0:
		tmp = t_1
	elif t <= -3.45e-292:
		tmp = x + (a / ((1.0 - z) / z))
	elif t <= 5e-86:
		tmp = x - (y * a)
	elif t <= 7e-11:
		tmp = x - a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(a / t) * Float64(z - y)))
	tmp = 0.0
	if (t <= -3300000000.0)
		tmp = t_1;
	elseif (t <= -3.45e-292)
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 - z) / z)));
	elseif (t <= 5e-86)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 7e-11)
		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 / t) * (z - y));
	tmp = 0.0;
	if (t <= -3300000000.0)
		tmp = t_1;
	elseif (t <= -3.45e-292)
		tmp = x + (a / ((1.0 - z) / z));
	elseif (t <= 5e-86)
		tmp = x - (y * a);
	elseif (t <= 7e-11)
		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[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3300000000.0], t$95$1, If[LessEqual[t, -3.45e-292], N[(x + N[(a / N[(N[(1.0 - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-86], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-11], N[(x - a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.3e9 or 7.00000000000000038e-11 < t

   1. Initial program 97.0%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in t around inf 78.2%

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

      1. associate-/l* 83.8%

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

      2. associate-/r/ 86.1%

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

   6. Simplified 86.1%

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

   if -3.3e9 < t < -3.44999999999999984e-292

   1. Initial program 96.1%

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

      1. associate-/r/ 96.1%

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

      2. div-inv 96.1%

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

      3. associate-/r* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around 0 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-/l* 96.1%

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

   8. Simplified 96.1%

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

   9. Taylor expanded in y around 0 59.0%

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

       1. sub-neg 59.0%

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

       2. mul-1-neg 59.0%

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

       3. *-commutative 59.0%

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

       4. associate-*r/ 73.8%

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

       5. remove-double-neg 73.8%

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

       6. *-commutative 73.8%

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

       7. associate-/r/ 75.7%

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

   11. Simplified 75.7%

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

   if -3.44999999999999984e-292 < t < 4.9999999999999999e-86

   1. Initial program 95.0%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

      1. associate-/r/ 95.0%

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

      2. div-inv 95.0%

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

      3. associate-/r* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around 0 94.8%

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

      1. *-commutative 94.8%

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

      2. associate-/l* 95.0%

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

   8. Simplified 95.0%

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

   9. Taylor expanded in z around 0 70.3%

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

   if 4.9999999999999999e-86 < t < 7.00000000000000038e-11

   1. Initial program 94.6%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 89.3%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3300000000:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-292}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-86}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-11}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \end{array} \]

Alternative 3: 71.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+120}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-285}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+71}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+120)
   (- x a)
   (if (<= z -1.22e-25)
     x
     (if (<= z 3.8e-285)
       (- x (* y a))
       (if (<= z 3e+71) (- x (* a (/ y t))) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+120) {
		tmp = x - a;
	} else if (z <= -1.22e-25) {
		tmp = x;
	} else if (z <= 3.8e-285) {
		tmp = x - (y * a);
	} else if (z <= 3e+71) {
		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) :: tmp
    if (z <= (-6.5d+120)) then
        tmp = x - a
    else if (z <= (-1.22d-25)) then
        tmp = x
    else if (z <= 3.8d-285) then
        tmp = x - (y * a)
    else if (z <= 3d+71) 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 tmp;
	if (z <= -6.5e+120) {
		tmp = x - a;
	} else if (z <= -1.22e-25) {
		tmp = x;
	} else if (z <= 3.8e-285) {
		tmp = x - (y * a);
	} else if (z <= 3e+71) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+120:
		tmp = x - a
	elif z <= -1.22e-25:
		tmp = x
	elif z <= 3.8e-285:
		tmp = x - (y * a)
	elif z <= 3e+71:
		tmp = x - (a * (y / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+120)
		tmp = Float64(x - a);
	elseif (z <= -1.22e-25)
		tmp = x;
	elseif (z <= 3.8e-285)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 3e+71)
		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)
	tmp = 0.0;
	if (z <= -6.5e+120)
		tmp = x - a;
	elseif (z <= -1.22e-25)
		tmp = x;
	elseif (z <= 3.8e-285)
		tmp = x - (y * a);
	elseif (z <= 3e+71)
		tmp = x - (a * (y / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+120], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.22e-25], x, If[LessEqual[z, 3.8e-285], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+71], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.4999999999999997e120 or 3.00000000000000013e71 < z

   1. Initial program 90.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 84.3%

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

   if -6.4999999999999997e120 < z < -1.21999999999999999e-25

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

      2. div-inv 99.9%

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

      3. associate-/r* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around 0 66.0%

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

      1. *-commutative 66.0%

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

      2. associate-/l* 68.6%

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

   8. Simplified 68.6%

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

   9. Taylor expanded in x around inf 70.2%

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

   if -1.21999999999999999e-25 < z < 3.8000000000000002e-285

   1. Initial program 99.8%

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

      1. associate-/r/ 98.0%

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

   3. Simplified 98.0%

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

      1. associate-/r/ 99.8%

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

      2. div-inv 99.8%

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

      3. associate-/r* 97.9%

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

   5. Applied egg-rr 97.9%

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

   6. Taylor expanded in t around 0 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/l* 79.3%

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

   8. Simplified 79.3%

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

   9. Taylor expanded in z around 0 79.6%

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

   if 3.8000000000000002e-285 < z < 3.00000000000000013e71

   1. Initial program 98.7%

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

      1. associate-/r/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in t around inf 73.6%

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

   5. Taylor expanded in y around inf 71.3%

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

      1. associate-/l* 75.5%

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

      2. associate-/r/ 76.8%

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

   7. Simplified 76.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+120}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-285}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+71}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 4: 72.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+69}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-284}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+71}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.1e+69)
   (- x a)
   (if (<= z -8e-89)
     (- x (/ (* y a) t))
     (if (<= z 3.7e-284)
       (- x (* y a))
       (if (<= z 5.2e+71) (- x (* a (/ y t))) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.1e+69) {
		tmp = x - a;
	} else if (z <= -8e-89) {
		tmp = x - ((y * a) / t);
	} else if (z <= 3.7e-284) {
		tmp = x - (y * a);
	} else if (z <= 5.2e+71) {
		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) :: tmp
    if (z <= (-5.1d+69)) then
        tmp = x - a
    else if (z <= (-8d-89)) then
        tmp = x - ((y * a) / t)
    else if (z <= 3.7d-284) then
        tmp = x - (y * a)
    else if (z <= 5.2d+71) 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 tmp;
	if (z <= -5.1e+69) {
		tmp = x - a;
	} else if (z <= -8e-89) {
		tmp = x - ((y * a) / t);
	} else if (z <= 3.7e-284) {
		tmp = x - (y * a);
	} else if (z <= 5.2e+71) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.1e+69:
		tmp = x - a
	elif z <= -8e-89:
		tmp = x - ((y * a) / t)
	elif z <= 3.7e-284:
		tmp = x - (y * a)
	elif z <= 5.2e+71:
		tmp = x - (a * (y / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.1e+69)
		tmp = Float64(x - a);
	elseif (z <= -8e-89)
		tmp = Float64(x - Float64(Float64(y * a) / t));
	elseif (z <= 3.7e-284)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 5.2e+71)
		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)
	tmp = 0.0;
	if (z <= -5.1e+69)
		tmp = x - a;
	elseif (z <= -8e-89)
		tmp = x - ((y * a) / t);
	elseif (z <= 3.7e-284)
		tmp = x - (y * a);
	elseif (z <= 5.2e+71)
		tmp = x - (a * (y / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.1e+69], N[(x - a), $MachinePrecision], If[LessEqual[z, -8e-89], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-284], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+71], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.09999999999999999e69 or 5.19999999999999983e71 < z

   1. Initial program 91.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 82.5%

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

   if -5.09999999999999999e69 < z < -8.00000000000000031e-89

   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. Taylor expanded in t around inf 64.2%

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

   5. Taylor expanded in y around inf 72.9%

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

   if -8.00000000000000031e-89 < z < 3.7e-284

   1. Initial program 99.8%

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

      1. associate-/r/ 97.5%

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

   3. Simplified 97.5%

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

      1. associate-/r/ 99.8%

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

      2. div-inv 99.8%

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

      3. associate-/r* 97.4%

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

   5. Applied egg-rr 97.4%

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

   6. Taylor expanded in t around 0 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-/l* 81.8%

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

   8. Simplified 81.8%

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

   9. Taylor expanded in z around 0 82.0%

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

   if 3.7e-284 < z < 5.19999999999999983e71

   1. Initial program 98.7%

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

      1. associate-/r/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in t around inf 73.6%

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

   5. Taylor expanded in y around inf 71.3%

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

      1. associate-/l* 75.5%

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

      2. associate-/r/ 76.8%

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

   7. Simplified 76.8%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+69}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-284}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+71}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 5: 72.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+120}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-284}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+71}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+120)
   (- x a)
   (if (<= z -1.0)
     (+ x (* y (/ a z)))
     (if (<= z 1.9e-284)
       (- x (* y a))
       (if (<= z 3e+71) (- x (* a (/ y t))) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+120) {
		tmp = x - a;
	} else if (z <= -1.0) {
		tmp = x + (y * (a / z));
	} else if (z <= 1.9e-284) {
		tmp = x - (y * a);
	} else if (z <= 3e+71) {
		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) :: tmp
    if (z <= (-6.8d+120)) then
        tmp = x - a
    else if (z <= (-1.0d0)) then
        tmp = x + (y * (a / z))
    else if (z <= 1.9d-284) then
        tmp = x - (y * a)
    else if (z <= 3d+71) 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 tmp;
	if (z <= -6.8e+120) {
		tmp = x - a;
	} else if (z <= -1.0) {
		tmp = x + (y * (a / z));
	} else if (z <= 1.9e-284) {
		tmp = x - (y * a);
	} else if (z <= 3e+71) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+120:
		tmp = x - a
	elif z <= -1.0:
		tmp = x + (y * (a / z))
	elif z <= 1.9e-284:
		tmp = x - (y * a)
	elif z <= 3e+71:
		tmp = x - (a * (y / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+120)
		tmp = Float64(x - a);
	elseif (z <= -1.0)
		tmp = Float64(x + Float64(y * Float64(a / z)));
	elseif (z <= 1.9e-284)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 3e+71)
		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)
	tmp = 0.0;
	if (z <= -6.8e+120)
		tmp = x - a;
	elseif (z <= -1.0)
		tmp = x + (y * (a / z));
	elseif (z <= 1.9e-284)
		tmp = x - (y * a);
	elseif (z <= 3e+71)
		tmp = x - (a * (y / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+120], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.0], N[(x + N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-284], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+71], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.79999999999999998e120 or 3.00000000000000013e71 < z

   1. Initial program 90.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 84.3%

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

   if -6.79999999999999998e120 < z < -1

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. distribute-neg-frac 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in y around inf 71.4%

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

      1. *-commutative 71.4%

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

      2. associate-*r/ 74.1%

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

      3. associate-*r* 74.1%

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

      4. neg-mul-1 74.1%

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

   7. Simplified 74.1%

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

   if -1 < z < 1.8999999999999999e-284

   1. Initial program 99.8%

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

      1. associate-/r/ 98.1%

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

   3. Simplified 98.1%

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

      1. associate-/r/ 99.8%

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

      2. div-inv 99.8%

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

      3. associate-/r* 98.0%

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

   5. Applied egg-rr 98.0%

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

   6. Taylor expanded in t around 0 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-/l* 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in z around 0 78.5%

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

   if 1.8999999999999999e-284 < z < 3.00000000000000013e71

   1. Initial program 98.7%

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

      1. associate-/r/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in t around inf 73.6%

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

   5. Taylor expanded in y around inf 71.3%

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

      1. associate-/l* 75.5%

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

      2. associate-/r/ 76.8%

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

   7. Simplified 76.8%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+120}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x + y \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-284}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+71}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 6: 72.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+121}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x - \frac{a}{\frac{-z}{y}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-284}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+72}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+121)
   (- x a)
   (if (<= z -1.0)
     (- x (/ a (/ (- z) y)))
     (if (<= z 2.1e-284)
       (- x (* y a))
       (if (<= z 1.55e+72) (- x (* a (/ y t))) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+121) {
		tmp = x - a;
	} else if (z <= -1.0) {
		tmp = x - (a / (-z / y));
	} else if (z <= 2.1e-284) {
		tmp = x - (y * a);
	} else if (z <= 1.55e+72) {
		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) :: tmp
    if (z <= (-1.35d+121)) then
        tmp = x - a
    else if (z <= (-1.0d0)) then
        tmp = x - (a / (-z / y))
    else if (z <= 2.1d-284) then
        tmp = x - (y * a)
    else if (z <= 1.55d+72) 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 tmp;
	if (z <= -1.35e+121) {
		tmp = x - a;
	} else if (z <= -1.0) {
		tmp = x - (a / (-z / y));
	} else if (z <= 2.1e-284) {
		tmp = x - (y * a);
	} else if (z <= 1.55e+72) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e+121:
		tmp = x - a
	elif z <= -1.0:
		tmp = x - (a / (-z / y))
	elif z <= 2.1e-284:
		tmp = x - (y * a)
	elif z <= 1.55e+72:
		tmp = x - (a * (y / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+121)
		tmp = Float64(x - a);
	elseif (z <= -1.0)
		tmp = Float64(x - Float64(a / Float64(Float64(-z) / y)));
	elseif (z <= 2.1e-284)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 1.55e+72)
		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)
	tmp = 0.0;
	if (z <= -1.35e+121)
		tmp = x - a;
	elseif (z <= -1.0)
		tmp = x - (a / (-z / y));
	elseif (z <= 2.1e-284)
		tmp = x - (y * a);
	elseif (z <= 1.55e+72)
		tmp = x - (a * (y / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+121], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.0], N[(x - N[(a / N[((-z) / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-284], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+72], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3500000000000001e121 or 1.54999999999999994e72 < z

   1. Initial program 90.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 84.3%

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

   if -1.3500000000000001e121 < z < -1

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 91.4%

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

      1. *-commutative 91.4%

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

      2. associate-/l* 96.9%

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

      3. associate--l+ 96.9%

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

   6. Simplified 96.9%

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

   7. Taylor expanded in z around inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. distribute-neg-frac 74.2%

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

   9. Simplified 74.2%

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

   if -1 < z < 2.09999999999999991e-284

   1. Initial program 99.8%

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

      1. associate-/r/ 98.1%

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

   3. Simplified 98.1%

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

      1. associate-/r/ 99.8%

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

      2. div-inv 99.8%

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

      3. associate-/r* 98.0%

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

   5. Applied egg-rr 98.0%

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

   6. Taylor expanded in t around 0 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-/l* 80.2%

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

   8. Simplified 80.2%

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

   9. Taylor expanded in z around 0 78.5%

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

   if 2.09999999999999991e-284 < z < 1.54999999999999994e72

   1. Initial program 98.7%

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

      1. associate-/r/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in t around inf 73.6%

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

   5. Taylor expanded in y around inf 71.3%

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

      1. associate-/l* 75.5%

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

      2. associate-/r/ 76.8%

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

   7. Simplified 76.8%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+121}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x - \frac{a}{\frac{-z}{y}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-284}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+72}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 7: 75.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-284}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+67}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- (* y (/ a z)) a))))
   (if (<= z -4.5e+26)
     t_1
     (if (<= z 1.8e-284)
       (- x (* y a))
       (if (<= z 5e+67) (- x (* a (/ y t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (a / z)) - a);
	double tmp;
	if (z <= -4.5e+26) {
		tmp = t_1;
	} else if (z <= 1.8e-284) {
		tmp = x - (y * a);
	} else if (z <= 5e+67) {
		tmp = x - (a * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * (a / z)) - a)
    if (z <= (-4.5d+26)) then
        tmp = t_1
    else if (z <= 1.8d-284) then
        tmp = x - (y * a)
    else if (z <= 5d+67) then
        tmp = x - (a * (y / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (a / z)) - a);
	double tmp;
	if (z <= -4.5e+26) {
		tmp = t_1;
	} else if (z <= 1.8e-284) {
		tmp = x - (y * a);
	} else if (z <= 5e+67) {
		tmp = x - (a * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * (a / z)) - a)
	tmp = 0
	if z <= -4.5e+26:
		tmp = t_1
	elif z <= 1.8e-284:
		tmp = x - (y * a)
	elif z <= 5e+67:
		tmp = x - (a * (y / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * Float64(a / z)) - a))
	tmp = 0.0
	if (z <= -4.5e+26)
		tmp = t_1;
	elseif (z <= 1.8e-284)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 5e+67)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * (a / z)) - a);
	tmp = 0.0;
	if (z <= -4.5e+26)
		tmp = t_1;
	elseif (z <= 1.8e-284)
		tmp = x - (y * a);
	elseif (z <= 5e+67)
		tmp = x - (a * (y / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+26], t$95$1, If[LessEqual[z, 1.8e-284], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+67], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.49999999999999978e26 or 4.99999999999999976e67 < z

   1. Initial program 92.8%

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

   2. Taylor expanded in z around inf 80.1%

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

      1. mul-1-neg 80.1%

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

      2. distribute-neg-frac 80.1%

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

   4. Simplified 80.1%

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

   5. Taylor expanded in y around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. unsub-neg 81.7%

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

      3. *-commutative 81.7%

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

      4. associate-*r/ 85.6%

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

   7. Simplified 85.6%

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

   if -4.49999999999999978e26 < z < 1.8000000000000001e-284

   1. Initial program 99.8%

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

      1. associate-/r/ 98.3%

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

   3. Simplified 98.3%

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

      1. associate-/r/ 99.8%

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

      2. div-inv 99.8%

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

      3. associate-/r* 98.2%

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

   5. Applied egg-rr 98.2%

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

   6. Taylor expanded in t around 0 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 75.6%

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

   8. Simplified 75.6%

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

   9. Taylor expanded in z around 0 74.5%

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

   if 1.8000000000000001e-284 < z < 4.99999999999999976e67

   1. Initial program 98.7%

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

      1. associate-/r/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in t around inf 74.1%

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

   5. Taylor expanded in y around inf 72.8%

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

      1. associate-/l* 76.0%

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

      2. associate-/r/ 77.4%

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

   7. Simplified 77.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+26}:\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-284}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+67}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \end{array} \]

Alternative 8: 90.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+46} \lor \neg \left(t \leq 6.5 \cdot 10^{+31}\right):\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.75e+46) (not (<= t 6.5e+31)))
   (+ x (* (/ a t) (- z y)))
   (- x (* (- y z) (/ a (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.75e+46) || !(t <= 6.5e+31)) {
		tmp = x + ((a / t) * (z - y));
	} else {
		tmp = x - ((y - z) * (a / (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 <= (-1.75d+46)) .or. (.not. (t <= 6.5d+31))) then
        tmp = x + ((a / t) * (z - y))
    else
        tmp = x - ((y - z) * (a / (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 <= -1.75e+46) || !(t <= 6.5e+31)) {
		tmp = x + ((a / t) * (z - y));
	} else {
		tmp = x - ((y - z) * (a / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.75e+46) or not (t <= 6.5e+31):
		tmp = x + ((a / t) * (z - y))
	else:
		tmp = x - ((y - z) * (a / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.75e+46) || !(t <= 6.5e+31))
		tmp = Float64(x + Float64(Float64(a / t) * Float64(z - y)));
	else
		tmp = Float64(x - Float64(Float64(y - z) * Float64(a / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.75e+46) || ~((t <= 6.5e+31)))
		tmp = x + ((a / t) * (z - y));
	else
		tmp = x - ((y - z) * (a / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.75e+46], N[Not[LessEqual[t, 6.5e+31]], $MachinePrecision]], N[(x + N[(N[(a / t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.74999999999999992e46 or 6.5000000000000004e31 < t

   1. Initial program 97.4%

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

      1. associate-/r/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around inf 79.6%

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

      1. associate-/l* 86.0%

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

      2. associate-/r/ 88.6%

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

   6. Simplified 88.6%

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

   if -1.74999999999999992e46 < t < 6.5000000000000004e31

   1. Initial program 95.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around 0 86.5%

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

      1. associate-/l* 97.8%

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

      2. associate-/r/ 93.2%

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

   6. Simplified 93.2%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+46} \lor \neg \left(t \leq 6.5 \cdot 10^{+31}\right):\\ \;\;\;\;x + \frac{a}{t} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{1 - z}\\ \end{array} \]

Alternative 9: 89.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+121} \lor \neg \left(z \leq 8 \cdot 10^{+71}\right):\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{\left(t - z\right) + 1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.3e+121) (not (<= z 8e+71)))
   (+ x (- (* y (/ a z)) a))
   (- x (/ a (/ (+ (- t z) 1.0) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.3e+121) || !(z <= 8e+71)) {
		tmp = x + ((y * (a / z)) - a);
	} else {
		tmp = x - (a / (((t - z) + 1.0) / 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 <= (-2.3d+121)) .or. (.not. (z <= 8d+71))) then
        tmp = x + ((y * (a / z)) - a)
    else
        tmp = x - (a / (((t - z) + 1.0d0) / 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 <= -2.3e+121) || !(z <= 8e+71)) {
		tmp = x + ((y * (a / z)) - a);
	} else {
		tmp = x - (a / (((t - z) + 1.0) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.3e+121) or not (z <= 8e+71):
		tmp = x + ((y * (a / z)) - a)
	else:
		tmp = x - (a / (((t - z) + 1.0) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.3e+121) || !(z <= 8e+71))
		tmp = Float64(x + Float64(Float64(y * Float64(a / z)) - a));
	else
		tmp = Float64(x - Float64(a / Float64(Float64(Float64(t - z) + 1.0) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.3e+121) || ~((z <= 8e+71)))
		tmp = x + ((y * (a / z)) - a);
	else
		tmp = x - (a / (((t - z) + 1.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.3e+121], N[Not[LessEqual[z, 8e+71]], $MachinePrecision]], N[(x + N[(N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999999e121 or 8.0000000000000003e71 < z

   1. Initial program 90.5%

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

   2. Taylor expanded in z around inf 82.9%

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

      1. mul-1-neg 82.9%

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

      2. distribute-neg-frac 82.9%

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

   4. Simplified 82.9%

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

   5. Taylor expanded in y around 0 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

      3. *-commutative 86.0%

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

      4. associate-*r/ 90.3%

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

   7. Simplified 90.3%

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

   if -2.2999999999999999e121 < z < 8.0000000000000003e71

   1. Initial program 99.3%

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

      1. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around inf 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-/l* 95.0%

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

      3. associate--l+ 95.0%

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

   6. Simplified 95.0%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+121} \lor \neg \left(z \leq 8 \cdot 10^{+71}\right):\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{\left(t - z\right) + 1}{y}}\\ \end{array} \]

Alternative 10: 86.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+85} \lor \neg \left(z \leq 8.5 \cdot 10^{+41}\right):\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.28e+85) (not (<= z 8.5e+41)))
   (+ x (- (* y (/ a z)) a))
   (- x (/ (* y a) (+ t 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.28e+85) || !(z <= 8.5e+41)) {
		tmp = x + ((y * (a / z)) - 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 <= (-1.28d+85)) .or. (.not. (z <= 8.5d+41))) then
        tmp = x + ((y * (a / z)) - 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 <= -1.28e+85) || !(z <= 8.5e+41)) {
		tmp = x + ((y * (a / z)) - a);
	} else {
		tmp = x - ((y * a) / (t + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.28e+85) or not (z <= 8.5e+41):
		tmp = x + ((y * (a / z)) - a)
	else:
		tmp = x - ((y * a) / (t + 1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.28e+85) || !(z <= 8.5e+41))
		tmp = Float64(x + Float64(Float64(y * Float64(a / z)) - a));
	else
		tmp = Float64(x - Float64(Float64(y * a) / Float64(t + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.28e+85) || ~((z <= 8.5e+41)))
		tmp = x + ((y * (a / z)) - 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, -1.28e+85], N[Not[LessEqual[z, 8.5e+41]], $MachinePrecision]], N[(x + N[(N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * a), $MachinePrecision] / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.28000000000000004e85 or 8.49999999999999938e41 < z

   1. Initial program 92.1%

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

   2. Taylor expanded in z around inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. distribute-neg-frac 80.5%

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

   4. Simplified 80.5%

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

   5. Taylor expanded in y around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. unsub-neg 82.2%

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

      3. *-commutative 82.2%

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

      4. associate-*r/ 86.6%

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

   7. Simplified 86.6%

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

   if -1.28000000000000004e85 < z < 8.49999999999999938e41

   1. Initial program 99.2%

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

      1. associate-/r/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around 0 91.8%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+85} \lor \neg \left(z \leq 8.5 \cdot 10^{+41}\right):\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot a}{t + 1}\\ \end{array} \]

Alternative 11: 72.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+120}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+29}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+120)
   (- x a)
   (if (<= z -1.65e-22) x (if (<= z 9.8e+29) (- x (* y a)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+120) {
		tmp = x - a;
	} else if (z <= -1.65e-22) {
		tmp = x;
	} else if (z <= 9.8e+29) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.5d+120)) then
        tmp = x - a
    else if (z <= (-1.65d-22)) then
        tmp = x
    else if (z <= 9.8d+29) then
        tmp = x - (y * a)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+120) {
		tmp = x - a;
	} else if (z <= -1.65e-22) {
		tmp = x;
	} else if (z <= 9.8e+29) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+120:
		tmp = x - a
	elif z <= -1.65e-22:
		tmp = x
	elif z <= 9.8e+29:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+120)
		tmp = Float64(x - a);
	elseif (z <= -1.65e-22)
		tmp = x;
	elseif (z <= 9.8e+29)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e+120)
		tmp = x - a;
	elseif (z <= -1.65e-22)
		tmp = x;
	elseif (z <= 9.8e+29)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+120], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.65e-22], x, If[LessEqual[z, 9.8e+29], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000009e120 or 9.8000000000000003e29 < z

   1. Initial program 91.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 81.4%

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

   if -2.50000000000000009e120 < z < -1.65e-22

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

      2. div-inv 99.9%

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

      3. associate-/r* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around 0 66.0%

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

      1. *-commutative 66.0%

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

      2. associate-/l* 68.6%

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

   8. Simplified 68.6%

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

   9. Taylor expanded in x around inf 70.2%

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

   if -1.65e-22 < z < 9.8000000000000003e29

   1. Initial program 99.0%

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

      1. associate-/r/ 98.3%

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

   3. Simplified 98.3%

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

      1. associate-/r/ 99.0%

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

      2. div-inv 99.1%

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

      3. associate-/r* 98.2%

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

   5. Applied egg-rr 98.2%

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

   6. Taylor expanded in t around 0 68.5%

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

      1. *-commutative 68.5%

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

      2. associate-/l* 68.4%

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

   8. Simplified 68.4%

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

   9. Taylor expanded in z around 0 67.1%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+120}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+29}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 12: 65.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+120}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+120) (- x a) (if (<= z 2.7e+34) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+120) {
		tmp = x - a;
	} else if (z <= 2.7e+34) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.5d+120)) then
        tmp = x - a
    else if (z <= 2.7d+34) then
        tmp = x
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+120) {
		tmp = x - a;
	} else if (z <= 2.7e+34) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+120:
		tmp = x - a
	elif z <= 2.7e+34:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+120)
		tmp = Float64(x - a);
	elseif (z <= 2.7e+34)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+120)
		tmp = x - a;
	elseif (z <= 2.7e+34)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+120], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.7e+34], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4999999999999997e120 or 2.7e34 < z

   1. Initial program 91.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 81.4%

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

   if -6.4999999999999997e120 < z < 2.7e34

   1. Initial program 99.2%

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

      1. associate-/r/ 98.7%

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

   3. Simplified 98.7%

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

      1. associate-/r/ 99.2%

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

      2. div-inv 99.3%

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

      3. associate-/r* 98.6%

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

   5. Applied egg-rr 98.6%

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

   6. Taylor expanded in t around 0 67.9%

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

      1. *-commutative 67.9%

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

      2. associate-/l* 68.5%

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

   8. Simplified 68.5%

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

   9. Taylor expanded in x around inf 60.0%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+120}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 13: 54.0% 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 96.2%

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

   1. associate-/r/ 99.2%

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

3. Simplified 99.2%

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

   1. associate-/r/ 96.2%

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

   2. div-inv 96.2%

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

   3. associate-/r* 99.0%

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

5. Applied egg-rr 99.0%

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

6. Taylor expanded in t around 0 67.7%

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

   1. *-commutative 67.7%

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

   2. associate-/l* 72.8%

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

8. Simplified 72.8%

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

9. Taylor expanded in x around inf 53.8%

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

10. Final simplification 53.8%

    \[\leadsto x \]

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 2023185 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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