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

Percentage Accurate: 97.4% → 99.6%

Time: 10.8s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.4% 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 97.9%

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

   1. associate-/r/ 99.9%

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

   2. *-commutative 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 77.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{1 - z}\\ t_2 := x + a \cdot \frac{z - y}{t}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-295}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{z}{\frac{1 - z}{a}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y (- 1.0 z))))) (t_2 (+ x (* a (/ (- z y) t)))))
   (if (<= t -8.5e+36)
     t_2
     (if (<= t -1.85e-266)
       t_1
       (if (<= t -1.2e-295)
         (- x a)
         (if (<= t 5.5e+18)
           t_1
           (if (<= t 4.4e+153) (+ x (/ z (/ (- 1.0 z) a))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / (1.0 - z)));
	double t_2 = x + (a * ((z - y) / t));
	double tmp;
	if (t <= -8.5e+36) {
		tmp = t_2;
	} else if (t <= -1.85e-266) {
		tmp = t_1;
	} else if (t <= -1.2e-295) {
		tmp = x - a;
	} else if (t <= 5.5e+18) {
		tmp = t_1;
	} else if (t <= 4.4e+153) {
		tmp = x + (z / ((1.0 - z) / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (a * (y / (1.0d0 - z)))
    t_2 = x + (a * ((z - y) / t))
    if (t <= (-8.5d+36)) then
        tmp = t_2
    else if (t <= (-1.85d-266)) then
        tmp = t_1
    else if (t <= (-1.2d-295)) then
        tmp = x - a
    else if (t <= 5.5d+18) then
        tmp = t_1
    else if (t <= 4.4d+153) then
        tmp = x + (z / ((1.0d0 - z) / a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / (1.0 - z)));
	double t_2 = x + (a * ((z - y) / t));
	double tmp;
	if (t <= -8.5e+36) {
		tmp = t_2;
	} else if (t <= -1.85e-266) {
		tmp = t_1;
	} else if (t <= -1.2e-295) {
		tmp = x - a;
	} else if (t <= 5.5e+18) {
		tmp = t_1;
	} else if (t <= 4.4e+153) {
		tmp = x + (z / ((1.0 - z) / a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (y / (1.0 - z)))
	t_2 = x + (a * ((z - y) / t))
	tmp = 0
	if t <= -8.5e+36:
		tmp = t_2
	elif t <= -1.85e-266:
		tmp = t_1
	elif t <= -1.2e-295:
		tmp = x - a
	elif t <= 5.5e+18:
		tmp = t_1
	elif t <= 4.4e+153:
		tmp = x + (z / ((1.0 - z) / a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / Float64(1.0 - z))))
	t_2 = Float64(x + Float64(a * Float64(Float64(z - y) / t)))
	tmp = 0.0
	if (t <= -8.5e+36)
		tmp = t_2;
	elseif (t <= -1.85e-266)
		tmp = t_1;
	elseif (t <= -1.2e-295)
		tmp = Float64(x - a);
	elseif (t <= 5.5e+18)
		tmp = t_1;
	elseif (t <= 4.4e+153)
		tmp = Float64(x + Float64(z / Float64(Float64(1.0 - z) / a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (y / (1.0 - z)));
	t_2 = x + (a * ((z - y) / t));
	tmp = 0.0;
	if (t <= -8.5e+36)
		tmp = t_2;
	elseif (t <= -1.85e-266)
		tmp = t_1;
	elseif (t <= -1.2e-295)
		tmp = x - a;
	elseif (t <= 5.5e+18)
		tmp = t_1;
	elseif (t <= 4.4e+153)
		tmp = x + (z / ((1.0 - z) / a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+36], t$95$2, If[LessEqual[t, -1.85e-266], t$95$1, If[LessEqual[t, -1.2e-295], N[(x - a), $MachinePrecision], If[LessEqual[t, 5.5e+18], t$95$1, If[LessEqual[t, 4.4e+153], N[(x + N[(z / N[(N[(1.0 - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.50000000000000014e36 or 4.3999999999999999e153 < t

   1. Initial program 96.5%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 87.1%

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

   if -8.50000000000000014e36 < t < -1.8500000000000001e-266 or -1.1999999999999999e-295 < t < 5.5e18

   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%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 99.5%

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

   5. Taylor expanded in y around inf 81.3%

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

   if -1.8500000000000001e-266 < t < -1.1999999999999999e-295

   1. Initial program 82.0%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 82.5%

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

   if 5.5e18 < t < 4.3999999999999999e153

   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%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 80.0%

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

   5. Taylor expanded in y around 0 62.0%

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

      1. sub-neg 62.0%

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

      2. mul-1-neg 62.0%

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

      3. remove-double-neg 62.0%

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

      4. *-commutative 62.0%

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

      5. associate-/l* 75.9%

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

   7. Simplified 75.9%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{1 - z}{a}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+36}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-266}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-295}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+18}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{z}{\frac{1 - z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]

Alternative 3: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{a}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+29}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-25}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ a (/ t y)))))
   (if (<= z -3.4e+29)
     (- x a)
     (if (<= z -2.9e-161)
       t_1
       (if (<= z 3.5e-25) (- x (* a y)) (if (<= z 5.2e+46) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a / (t / y));
	double tmp;
	if (z <= -3.4e+29) {
		tmp = x - a;
	} else if (z <= -2.9e-161) {
		tmp = t_1;
	} else if (z <= 3.5e-25) {
		tmp = x - (a * y);
	} else if (z <= 5.2e+46) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (a / (t / y))
    if (z <= (-3.4d+29)) then
        tmp = x - a
    else if (z <= (-2.9d-161)) then
        tmp = t_1
    else if (z <= 3.5d-25) then
        tmp = x - (a * y)
    else if (z <= 5.2d+46) then
        tmp = t_1
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a / (t / y));
	double tmp;
	if (z <= -3.4e+29) {
		tmp = x - a;
	} else if (z <= -2.9e-161) {
		tmp = t_1;
	} else if (z <= 3.5e-25) {
		tmp = x - (a * y);
	} else if (z <= 5.2e+46) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a / (t / y))
	tmp = 0
	if z <= -3.4e+29:
		tmp = x - a
	elif z <= -2.9e-161:
		tmp = t_1
	elif z <= 3.5e-25:
		tmp = x - (a * y)
	elif z <= 5.2e+46:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a / Float64(t / y)))
	tmp = 0.0
	if (z <= -3.4e+29)
		tmp = Float64(x - a);
	elseif (z <= -2.9e-161)
		tmp = t_1;
	elseif (z <= 3.5e-25)
		tmp = Float64(x - Float64(a * y));
	elseif (z <= 5.2e+46)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a / (t / y));
	tmp = 0.0;
	if (z <= -3.4e+29)
		tmp = x - a;
	elseif (z <= -2.9e-161)
		tmp = t_1;
	elseif (z <= 3.5e-25)
		tmp = x - (a * y);
	elseif (z <= 5.2e+46)
		tmp = t_1;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+29], N[(x - a), $MachinePrecision], If[LessEqual[z, -2.9e-161], t$95$1, If[LessEqual[z, 3.5e-25], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+46], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.39999999999999981e29 or 5.20000000000000027e46 < z

   1. Initial program 95.8%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.7%

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

   if -3.39999999999999981e29 < z < -2.9e-161 or 3.5000000000000002e-25 < z < 5.20000000000000027e46

   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%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 73.6%

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

   5. Taylor expanded in y around inf 74.6%

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

      1. *-commutative 74.6%

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

      2. associate-/l* 80.1%

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

   7. Simplified 80.1%

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

   if -2.9e-161 < z < 3.5000000000000002e-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/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 82.7%

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

   5. Taylor expanded in z around 0 80.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+29}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-161}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-25}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+46}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 4: 90.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+124} \lor \neg \left(t \leq 1.15 \cdot 10^{+129}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.1e+124) (not (<= t 1.15e+129)))
   (+ x (* a (/ (- z y) t)))
   (+ x (* a (/ (- z y) (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.1e+124) || !(t <= 1.15e+129)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x + (a * ((z - y) / (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 <= (-3.1d+124)) .or. (.not. (t <= 1.15d+129))) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = x + (a * ((z - y) / (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 <= -3.1e+124) || !(t <= 1.15e+129)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.1e+124) or not (t <= 1.15e+129):
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x + (a * ((z - y) / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.1e+124) || !(t <= 1.15e+129))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.1e+124) || ~((t <= 1.15e+129)))
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x + (a * ((z - y) / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.1e+124], N[Not[LessEqual[t, 1.15e+129]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1000000000000002e124 or 1.14999999999999995e129 < t

   1. Initial program 96.2%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 88.6%

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

   if -3.1000000000000002e124 < t < 1.14999999999999995e129

   1. Initial program 98.7%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 95.5%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+124} \lor \neg \left(t \leq 1.15 \cdot 10^{+129}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \]

Alternative 5: 87.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+33} \lor \neg \left(z \leq 1.48 \cdot 10^{+34}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.2e+33) (not (<= z 1.48e+34)))
   (+ x (/ (- z y) (/ (- z) a)))
   (- x (/ a (/ (+ t 1.0) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.2e+33) || !(z <= 1.48e+34)) {
		tmp = x + ((z - y) / (-z / a));
	} else {
		tmp = x - (a / ((t + 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 <= (-9.2d+33)) .or. (.not. (z <= 1.48d+34))) then
        tmp = x + ((z - y) / (-z / a))
    else
        tmp = x - (a / ((t + 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 <= -9.2e+33) || !(z <= 1.48e+34)) {
		tmp = x + ((z - y) / (-z / a));
	} else {
		tmp = x - (a / ((t + 1.0) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.2e+33) or not (z <= 1.48e+34):
		tmp = x + ((z - y) / (-z / a))
	else:
		tmp = x - (a / ((t + 1.0) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.2e+33) || !(z <= 1.48e+34))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(-z) / a)));
	else
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.2e+33) || ~((z <= 1.48e+34)))
		tmp = x + ((z - y) / (-z / a));
	else
		tmp = x - (a / ((t + 1.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.2e+33], N[Not[LessEqual[z, 1.48e+34]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.20000000000000042e33 or 1.4799999999999999e34 < z

   1. Initial program 95.9%

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

   2. Taylor expanded in z around inf 86.9%

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

      1. mul-1-neg 86.9%

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

      2. distribute-neg-frac 86.9%

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

   4. Simplified 86.9%

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

   if -9.20000000000000042e33 < z < 1.4799999999999999e34

   1. Initial program 99.9%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 89.4%

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

      1. associate-/l* 94.3%

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

   6. Simplified 94.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+33} \lor \neg \left(z \leq 1.48 \cdot 10^{+34}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \]

Alternative 6: 88.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+34}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+30)
   (+ x (/ a (/ (+ (- t z) 1.0) z)))
   (if (<= z 1.1e+34)
     (- x (/ a (/ (+ t 1.0) y)))
     (+ x (/ (- z y) (/ (- z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+30) {
		tmp = x + (a / (((t - z) + 1.0) / z));
	} else if (z <= 1.1e+34) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x + ((z - y) / (-z / 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 <= (-2.3d+30)) then
        tmp = x + (a / (((t - z) + 1.0d0) / z))
    else if (z <= 1.1d+34) then
        tmp = x - (a / ((t + 1.0d0) / y))
    else
        tmp = x + ((z - y) / (-z / 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 <= -2.3e+30) {
		tmp = x + (a / (((t - z) + 1.0) / z));
	} else if (z <= 1.1e+34) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x + ((z - y) / (-z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+30:
		tmp = x + (a / (((t - z) + 1.0) / z))
	elif z <= 1.1e+34:
		tmp = x - (a / ((t + 1.0) / y))
	else:
		tmp = x + ((z - y) / (-z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+30)
		tmp = Float64(x + Float64(a / Float64(Float64(Float64(t - z) + 1.0) / z)));
	elseif (z <= 1.1e+34)
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	else
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(-z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.3e+30)
		tmp = x + (a / (((t - z) + 1.0) / z));
	elseif (z <= 1.1e+34)
		tmp = x - (a / ((t + 1.0) / y));
	else
		tmp = x + ((z - y) / (-z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+30], N[(x + N[(a / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+34], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - y), $MachinePrecision] / N[((-z) / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e30

   1. Initial program 95.0%

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

      1. clear-num 95.0%

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

      2. associate-/r/ 94.8%

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

   3. Applied egg-rr 94.8%

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

   4. Taylor expanded in y around 0 64.1%

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

      1. sub-neg 64.1%

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

      2. mul-1-neg 64.1%

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

      3. remove-double-neg 64.1%

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

      4. associate-/l* 86.5%

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

      5. associate--l+ 86.5%

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

   6. Simplified 86.5%

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

   if -2.3e30 < z < 1.1000000000000001e34

   1. Initial program 99.9%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 89.4%

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

      1. associate-/l* 94.3%

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

   6. Simplified 94.3%

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

   if 1.1000000000000001e34 < z

   1. Initial program 96.7%

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

   2. Taylor expanded in z around inf 91.1%

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

      1. mul-1-neg 91.1%

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

      2. distribute-neg-frac 91.1%

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

   4. Simplified 91.1%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+34}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \end{array} \]

Alternative 7: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+87}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 10^{+61}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.6e+87)
   (- x a)
   (if (<= z 1e+61) (- x (* a (/ y (- 1.0 z)))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+87) {
		tmp = x - a;
	} else if (z <= 1e+61) {
		tmp = x - (a * (y / (1.0 - z)));
	} 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 <= (-6.6d+87)) then
        tmp = x - a
    else if (z <= 1d+61) then
        tmp = x - (a * (y / (1.0d0 - z)))
    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 <= -6.6e+87) {
		tmp = x - a;
	} else if (z <= 1e+61) {
		tmp = x - (a * (y / (1.0 - z)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.6e+87:
		tmp = x - a
	elif z <= 1e+61:
		tmp = x - (a * (y / (1.0 - z)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.6e+87)
		tmp = Float64(x - a);
	elseif (z <= 1e+61)
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 - z))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.6e+87)
		tmp = x - a;
	elseif (z <= 1e+61)
		tmp = x - (a * (y / (1.0 - z)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.6e+87], N[(x - a), $MachinePrecision], If[LessEqual[z, 1e+61], N[(x - N[(a * N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6000000000000003e87 or 9.99999999999999949e60 < z

   1. Initial program 95.4%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 79.1%

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

   if -6.6000000000000003e87 < z < 9.99999999999999949e60

   1. Initial program 99.9%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 75.6%

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

   5. Taylor expanded in y around inf 75.2%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+87}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 10^{+61}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 8: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+32}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+34}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.1e+32)
   (- x a)
   (if (<= z 1.2e+34) (- x (/ a (/ (+ t 1.0) y))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.1e+32) {
		tmp = x - a;
	} else if (z <= 1.2e+34) {
		tmp = x - (a / ((t + 1.0) / y));
	} 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 <= (-6.1d+32)) then
        tmp = x - a
    else if (z <= 1.2d+34) then
        tmp = x - (a / ((t + 1.0d0) / y))
    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 <= -6.1e+32) {
		tmp = x - a;
	} else if (z <= 1.2e+34) {
		tmp = x - (a / ((t + 1.0) / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.1e+32:
		tmp = x - a
	elif z <= 1.2e+34:
		tmp = x - (a / ((t + 1.0) / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.1e+32)
		tmp = Float64(x - a);
	elseif (z <= 1.2e+34)
		tmp = Float64(x - Float64(a / Float64(Float64(t + 1.0) / y)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.1e+32)
		tmp = x - a;
	elseif (z <= 1.2e+34)
		tmp = x - (a / ((t + 1.0) / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.1e+32], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.2e+34], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.10000000000000027e32 or 1.19999999999999993e34 < z

   1. Initial program 95.9%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.4%

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

   if -6.10000000000000027e32 < z < 1.19999999999999993e34

   1. Initial program 99.9%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 89.4%

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

      1. associate-/l* 94.3%

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

   6. Simplified 94.3%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+32}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+34}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 9: 65.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-23}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e-23)
   (- x a)
   (if (<= z 3.7e-184)
     x
     (if (<= z 3.9e-123) (* a (- y)) (if (<= z 1.35e+34) x (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e-23) {
		tmp = x - a;
	} else if (z <= 3.7e-184) {
		tmp = x;
	} else if (z <= 3.9e-123) {
		tmp = a * -y;
	} else if (z <= 1.35e+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 <= (-1.6d-23)) then
        tmp = x - a
    else if (z <= 3.7d-184) then
        tmp = x
    else if (z <= 3.9d-123) then
        tmp = a * -y
    else if (z <= 1.35d+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 <= -1.6e-23) {
		tmp = x - a;
	} else if (z <= 3.7e-184) {
		tmp = x;
	} else if (z <= 3.9e-123) {
		tmp = a * -y;
	} else if (z <= 1.35e+34) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e-23:
		tmp = x - a
	elif z <= 3.7e-184:
		tmp = x
	elif z <= 3.9e-123:
		tmp = a * -y
	elif z <= 1.35e+34:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e-23)
		tmp = Float64(x - a);
	elseif (z <= 3.7e-184)
		tmp = x;
	elseif (z <= 3.9e-123)
		tmp = Float64(a * Float64(-y));
	elseif (z <= 1.35e+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 <= -1.6e-23)
		tmp = x - a;
	elseif (z <= 3.7e-184)
		tmp = x;
	elseif (z <= 3.9e-123)
		tmp = a * -y;
	elseif (z <= 1.35e+34)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e-23], N[(x - a), $MachinePrecision], If[LessEqual[z, 3.7e-184], x, If[LessEqual[z, 3.9e-123], N[(a * (-y)), $MachinePrecision], If[LessEqual[z, 1.35e+34], x, N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.59999999999999988e-23 or 1.35e34 < z

   1. Initial program 96.2%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 75.8%

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

   if -1.59999999999999988e-23 < z < 3.6999999999999999e-184 or 3.89999999999999976e-123 < z < 1.35e34

   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%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 65.3%

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

   if 3.6999999999999999e-184 < z < 3.89999999999999976e-123

   1. Initial program 99.7%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 75.6%

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

      1. associate-*r/ 75.6%

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

      2. *-commutative 75.6%

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

      3. associate-*r* 75.6%

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

      4. mul-1-neg 75.6%

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

      5. associate--l+ 75.6%

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

   6. Simplified 75.6%

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

   7. Taylor expanded in z around 0 75.6%

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

      1. associate-*r/ 75.6%

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

      2. mul-1-neg 75.6%

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

      3. *-commutative 75.6%

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

      4. distribute-rgt-neg-in 75.6%

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

   9. Simplified 75.6%

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

   10. Taylor expanded in t around 0 67.3%

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

       1. associate-*r* 67.3%

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

       2. mul-1-neg 67.3%

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

   12. Simplified 67.3%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-23}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 10: 73.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-10}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9.9 \cdot 10^{+33}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e-10) (- x a) (if (<= z 9.9e+33) (- x (* a y)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e-10) {
		tmp = x - a;
	} else if (z <= 9.9e+33) {
		tmp = x - (a * y);
	} 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 <= (-3.5d-10)) then
        tmp = x - a
    else if (z <= 9.9d+33) then
        tmp = x - (a * y)
    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 <= -3.5e-10) {
		tmp = x - a;
	} else if (z <= 9.9e+33) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e-10:
		tmp = x - a
	elif z <= 9.9e+33:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e-10)
		tmp = Float64(x - a);
	elseif (z <= 9.9e+33)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.5e-10)
		tmp = x - a;
	elseif (z <= 9.9e+33)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e-10], N[(x - a), $MachinePrecision], If[LessEqual[z, 9.9e+33], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4999999999999998e-10 or 9.89999999999999986e33 < z

   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%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.3%

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

   if -3.4999999999999998e-10 < z < 9.89999999999999986e33

   1. Initial program 99.9%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 76.5%

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

   5. Taylor expanded in z around 0 74.9%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-10}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9.9 \cdot 10^{+33}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 11: 67.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-23}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e-23) (- x a) (if (<= z 1.55e+34) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e-23) {
		tmp = x - a;
	} else if (z <= 1.55e+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 <= (-1.6d-23)) then
        tmp = x - a
    else if (z <= 1.55d+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 <= -1.6e-23) {
		tmp = x - a;
	} else if (z <= 1.55e+34) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e-23:
		tmp = x - a
	elif z <= 1.55e+34:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e-23)
		tmp = Float64(x - a);
	elseif (z <= 1.55e+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 <= -1.6e-23)
		tmp = x - a;
	elseif (z <= 1.55e+34)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e-23], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.55e+34], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999988e-23 or 1.54999999999999989e34 < z

   1. Initial program 96.2%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 75.8%

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

   if -1.59999999999999988e-23 < z < 1.54999999999999989e34

   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%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 60.7%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-23}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 12: 54.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

   1. associate-/r/ 99.9%

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

   2. *-commutative 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around inf 53.9%

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

5. Final simplification 53.9%

   \[\leadsto x \]

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 2023268 
(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))))