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

Percentage Accurate: 97.4% → 99.7%

Time: 10.1s

Alternatives: 11

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: 99.7% 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 97.1%

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

   1. associate-/r/ 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 72.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{1 - z}\\ \mathbf{if}\;z \leq -9.4 \cdot 10^{+63}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-191}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 170000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y (- 1.0 z))))))
   (if (<= z -9.4e+63)
     (- x a)
     (if (<= z -9.5e-85)
       t_1
       (if (<= z -5.8e-191)
         (- x (/ a (/ t y)))
         (if (<= z 170000.0) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / (1.0 - z)));
	double tmp;
	if (z <= -9.4e+63) {
		tmp = x - a;
	} else if (z <= -9.5e-85) {
		tmp = t_1;
	} else if (z <= -5.8e-191) {
		tmp = x - (a / (t / y));
	} else if (z <= 170000.0) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (a * (y / (1.0d0 - z)))
    if (z <= (-9.4d+63)) then
        tmp = x - a
    else if (z <= (-9.5d-85)) then
        tmp = t_1
    else if (z <= (-5.8d-191)) then
        tmp = x - (a / (t / y))
    else if (z <= 170000.0d0) then
        tmp = t_1
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / (1.0 - z)));
	double tmp;
	if (z <= -9.4e+63) {
		tmp = x - a;
	} else if (z <= -9.5e-85) {
		tmp = t_1;
	} else if (z <= -5.8e-191) {
		tmp = x - (a / (t / y));
	} else if (z <= 170000.0) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (y / (1.0 - z)))
	tmp = 0
	if z <= -9.4e+63:
		tmp = x - a
	elif z <= -9.5e-85:
		tmp = t_1
	elif z <= -5.8e-191:
		tmp = x - (a / (t / y))
	elif z <= 170000.0:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / Float64(1.0 - z))))
	tmp = 0.0
	if (z <= -9.4e+63)
		tmp = Float64(x - a);
	elseif (z <= -9.5e-85)
		tmp = t_1;
	elseif (z <= -5.8e-191)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (z <= 170000.0)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (y / (1.0 - z)));
	tmp = 0.0;
	if (z <= -9.4e+63)
		tmp = x - a;
	elseif (z <= -9.5e-85)
		tmp = t_1;
	elseif (z <= -5.8e-191)
		tmp = x - (a / (t / y));
	elseif (z <= 170000.0)
		tmp = t_1;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.4e+63], N[(x - a), $MachinePrecision], If[LessEqual[z, -9.5e-85], t$95$1, If[LessEqual[z, -5.8e-191], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 170000.0], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.4000000000000006e63 or 1.7e5 < z

   1. Initial program 93.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 83.3%

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

   if -9.4000000000000006e63 < z < -9.49999999999999964e-85 or -5.7999999999999999e-191 < z < 1.7e5

   1. Initial program 99.9%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around 0 83.6%

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

      1. associate-/l* 83.5%

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

      2. associate-/r/ 83.5%

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

   7. Simplified 83.5%

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

   8. Taylor expanded in y around inf 82.3%

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

      1. expm1-log1p-u 71.8%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a \cdot y}{1 - z}\right)\right)} \]

      2. expm1-udef 69.1%

         \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a \cdot y}{1 - z}\right)} - 1\right)} \]

   10. Applied egg-rr 69.1%

       \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a \cdot y}{1 - z}\right)} - 1\right)} \]
   11. Step-by-step derivation

       1. expm1-def 71.8%

          \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a \cdot y}{1 - z}\right)\right)} \]

       2. expm1-log1p 82.3%

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

       3. associate-*r/ 82.3%

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

   12. Simplified 82.3%

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

   if -9.49999999999999964e-85 < z < -5.7999999999999999e-191

   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. Add Preprocessing

   5. Taylor expanded in z around 0 96.0%

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

      1. associate-/l* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in t around inf 96.0%

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

      1. associate-/l* 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+63}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-85}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-191}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 170000:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+98} \lor \neg \left(t \leq 1.46 \cdot 10^{+26}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{1 - z} \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.6e+98) (not (<= t 1.46e+26)))
   (+ x (/ (- z y) (/ t a)))
   (+ x (* (/ a (- 1.0 z)) (- z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.6e+98) || !(t <= 1.46e+26)) {
		tmp = x + ((z - y) / (t / a));
	} else {
		tmp = x + ((a / (1.0 - z)) * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.6d+98)) .or. (.not. (t <= 1.46d+26))) then
        tmp = x + ((z - y) / (t / a))
    else
        tmp = x + ((a / (1.0d0 - z)) * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.6e+98) || !(t <= 1.46e+26)) {
		tmp = x + ((z - y) / (t / a));
	} else {
		tmp = x + ((a / (1.0 - z)) * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.6e+98) or not (t <= 1.46e+26):
		tmp = x + ((z - y) / (t / a))
	else:
		tmp = x + ((a / (1.0 - z)) * (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.6e+98) || !(t <= 1.46e+26))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	else
		tmp = Float64(x + Float64(Float64(a / Float64(1.0 - z)) * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.6e+98) || ~((t <= 1.46e+26)))
		tmp = x + ((z - y) / (t / a));
	else
		tmp = x + ((a / (1.0 - z)) * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.6e+98], N[Not[LessEqual[t, 1.46e+26]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.59999999999999981e98 or 1.45999999999999992e26 < t

   1. Initial program 98.8%

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

   3. Taylor expanded in t around inf 93.0%

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

   if -3.59999999999999981e98 < t < 1.45999999999999992e26

   1. Initial program 96.1%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 78.1%

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

      1. associate-/l* 97.0%

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

      2. associate-/r/ 93.7%

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

   7. Simplified 93.7%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+98} \lor \neg \left(t \leq 1.46 \cdot 10^{+26}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{1 - z} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.86 \cdot 10^{+99} \lor \neg \left(t \leq 6.1 \cdot 10^{+25}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.86e+99) (not (<= t 6.1e+25)))
   (+ x (/ (- z y) (/ t a)))
   (+ x (* a (/ (- z y) (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.86e+99) || !(t <= 6.1e+25)) {
		tmp = x + ((z - y) / (t / a));
	} 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 <= (-1.86d+99)) .or. (.not. (t <= 6.1d+25))) then
        tmp = x + ((z - y) / (t / a))
    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 <= -1.86e+99) || !(t <= 6.1e+25)) {
		tmp = x + ((z - y) / (t / a));
	} else {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.86e+99) or not (t <= 6.1e+25):
		tmp = x + ((z - y) / (t / a))
	else:
		tmp = x + (a * ((z - y) / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.86e+99) || !(t <= 6.1e+25))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(t / a)));
	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 <= -1.86e+99) || ~((t <= 6.1e+25)))
		tmp = x + ((z - y) / (t / a));
	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, -1.86e+99], N[Not[LessEqual[t, 6.1e+25]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[(t / a), $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 < -1.85999999999999999e99 or 6.1000000000000003e25 < t

   1. Initial program 98.8%

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

   3. Taylor expanded in t around inf 93.0%

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

   if -1.85999999999999999e99 < t < 6.1000000000000003e25

   1. Initial program 96.1%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 97.0%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.86 \cdot 10^{+99} \lor \neg \left(t \leq 6.1 \cdot 10^{+25}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+35}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-190}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-9}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e+35)
   (- x a)
   (if (<= z -1.35e-190)
     (- x (/ a (/ t y)))
     (if (<= z 6.4e-9) (- x (* y a)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+35) {
		tmp = x - a;
	} else if (z <= -1.35e-190) {
		tmp = x - (a / (t / y));
	} else if (z <= 6.4e-9) {
		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 <= (-1.95d+35)) then
        tmp = x - a
    else if (z <= (-1.35d-190)) then
        tmp = x - (a / (t / y))
    else if (z <= 6.4d-9) 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 <= -1.95e+35) {
		tmp = x - a;
	} else if (z <= -1.35e-190) {
		tmp = x - (a / (t / y));
	} else if (z <= 6.4e-9) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.95e+35:
		tmp = x - a
	elif z <= -1.35e-190:
		tmp = x - (a / (t / y))
	elif z <= 6.4e-9:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e+35)
		tmp = Float64(x - a);
	elseif (z <= -1.35e-190)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	elseif (z <= 6.4e-9)
		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 <= -1.95e+35)
		tmp = x - a;
	elseif (z <= -1.35e-190)
		tmp = x - (a / (t / y));
	elseif (z <= 6.4e-9)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e+35], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.35e-190], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e-9], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95e35 or 6.40000000000000023e-9 < z

   1. Initial program 93.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 81.5%

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

   if -1.95e35 < z < -1.35e-190

   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%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 92.7%

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

      1. associate-/l* 94.8%

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

   7. Simplified 94.8%

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

   8. Taylor expanded in t around inf 87.6%

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

      1. associate-/l* 89.7%

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

   10. Simplified 89.7%

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

   if -1.35e-190 < z < 6.40000000000000023e-9

   1. Initial program 99.9%

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

      1. associate-/r/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around 0 89.7%

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

      1. associate-/l* 91.6%

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

   7. Simplified 91.6%

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

   8. Taylor expanded in t around 0 79.9%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+35}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-190}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-9}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+35}:\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-8}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{-z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+35)
   (+ x (- (* y (/ a z)) a))
   (if (<= z 6.5e-8)
     (- x (* a (/ y (+ t 1.0))))
     (- x (/ a (/ (- z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+35) {
		tmp = x + ((y * (a / z)) - a);
	} else if (z <= 6.5e-8) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = x - (a / (-z / (y - 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 (z <= (-1.05d+35)) then
        tmp = x + ((y * (a / z)) - a)
    else if (z <= 6.5d-8) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else
        tmp = x - (a / (-z / (y - 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 (z <= -1.05e+35) {
		tmp = x + ((y * (a / z)) - a);
	} else if (z <= 6.5e-8) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = x - (a / (-z / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+35:
		tmp = x + ((y * (a / z)) - a)
	elif z <= 6.5e-8:
		tmp = x - (a * (y / (t + 1.0)))
	else:
		tmp = x - (a / (-z / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+35)
		tmp = Float64(x + Float64(Float64(y * Float64(a / z)) - a));
	elseif (z <= 6.5e-8)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	else
		tmp = Float64(x - Float64(a / Float64(Float64(-z) / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+35)
		tmp = x + ((y * (a / z)) - a);
	elseif (z <= 6.5e-8)
		tmp = x - (a * (y / (t + 1.0)));
	else
		tmp = x - (a / (-z / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+35], N[(x + N[(N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-8], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[((-z) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0499999999999999e35

   1. Initial program 97.1%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 62.6%

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

      1. associate-/l* 93.1%

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

      2. associate-/r/ 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in z around inf 90.2%

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

      1. associate-*r/ 90.2%

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

      2. neg-mul-1 90.2%

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

   10. Simplified 90.2%

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

   11. Taylor expanded in z around 0 85.0%

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

       1. mul-1-neg 85.0%

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

       2. unsub-neg 85.0%

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

       3. associate-*l/ 93.1%

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

       4. *-commutative 93.1%

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

   13. Simplified 93.1%

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

   if -1.0499999999999999e35 < z < 6.49999999999999997e-8

   1. Initial program 99.9%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 92.7%

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

   if 6.49999999999999997e-8 < z

   1. Initial program 90.6%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 68.6%

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

      1. associate-/l* 96.6%

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

      2. associate-/r/ 88.6%

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

   7. Simplified 88.6%

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

   8. Taylor expanded in z around inf 87.6%

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

      1. associate-*r/ 87.6%

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

      2. neg-mul-1 87.6%

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

   10. Simplified 87.6%

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

       1. associate-*l/ 67.6%

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

       2. frac-2neg 67.6%

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

       3. add-sqr-sqrt 33.6%

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

       4. sqrt-unprod 55.9%

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

       5. sqr-neg 55.9%

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

       6. sqrt-unprod 25.3%

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

       7. add-sqr-sqrt 40.7%

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

       8. distribute-lft-neg-out 40.7%

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

       9. add-sqr-sqrt 15.4%

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

       10. sqrt-unprod 47.8%

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

       11. sqr-neg 47.8%

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

       12. sqrt-unprod 33.9%

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

       13. add-sqr-sqrt 67.6%

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

   12. Applied egg-rr 67.6%

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

       1. associate-/l* 95.5%

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

   14. Simplified 95.5%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+35}:\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-8}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{-z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.9 \cdot 10^{+59} \lor \neg \left(z \leq 6.5 \cdot 10^{-8}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.9e+59) (not (<= z 6.5e-8)))
   (- x a)
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.9e+59) || !(z <= 6.5e-8)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / (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 <= (-7.9d+59)) .or. (.not. (z <= 6.5d-8))) then
        tmp = x - a
    else
        tmp = x - (a * (y / (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 <= -7.9e+59) || !(z <= 6.5e-8)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.9e+59) or not (z <= 6.5e-8):
		tmp = x - a
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.9e+59) || !(z <= 6.5e-8))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.9e+59) || ~((z <= 6.5e-8)))
		tmp = x - a;
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.9e+59], N[Not[LessEqual[z, 6.5e-8]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9000000000000001e59 or 6.49999999999999997e-8 < z

   1. Initial program 93.4%

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

   5. Taylor expanded in z around inf 82.8%

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

   if -7.9000000000000001e59 < z < 6.49999999999999997e-8

   1. Initial program 99.9%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 91.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.9 \cdot 10^{+59} \lor \neg \left(z \leq 6.5 \cdot 10^{-8}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+35} \lor \neg \left(z \leq 6.5 \cdot 10^{-8}\right):\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e+35) (not (<= z 6.5e-8)))
   (+ x (- (* y (/ a z)) a))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+35) || !(z <= 6.5e-8)) {
		tmp = x + ((y * (a / z)) - a);
	} else {
		tmp = x - (a * (y / (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 <= (-1.95d+35)) .or. (.not. (z <= 6.5d-8))) then
        tmp = x + ((y * (a / z)) - a)
    else
        tmp = x - (a * (y / (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 <= -1.95e+35) || !(z <= 6.5e-8)) {
		tmp = x + ((y * (a / z)) - a);
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e+35) or not (z <= 6.5e-8):
		tmp = x + ((y * (a / z)) - a)
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e+35) || !(z <= 6.5e-8))
		tmp = Float64(x + Float64(Float64(y * Float64(a / z)) - a));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.95e+35) || ~((z <= 6.5e-8)))
		tmp = x + ((y * (a / z)) - a);
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e+35], N[Not[LessEqual[z, 6.5e-8]], $MachinePrecision]], N[(x + N[(N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e35 or 6.49999999999999997e-8 < z

   1. Initial program 93.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 65.7%

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

      1. associate-/l* 94.9%

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

      2. associate-/r/ 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in z around inf 88.8%

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

      1. associate-*r/ 88.8%

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

      2. neg-mul-1 88.8%

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

   10. Simplified 88.8%

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

   11. Taylor expanded in z around 0 84.1%

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

       1. mul-1-neg 84.1%

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

       2. unsub-neg 84.1%

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

       3. associate-*l/ 93.6%

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

       4. *-commutative 93.6%

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

   13. Simplified 93.6%

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

   if -1.95e35 < z < 6.49999999999999997e-8

   1. Initial program 99.9%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 92.7%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+35} \lor \neg \left(z \leq 6.5 \cdot 10^{-8}\right):\\ \;\;\;\;x + \left(y \cdot \frac{a}{z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+59} \lor \neg \left(z \leq 6.4 \cdot 10^{-9}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e+59) (not (<= z 6.4e-9))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+59) || !(z <= 6.4e-9)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.5d+59)) .or. (.not. (z <= 6.4d-9))) then
        tmp = x - a
    else
        tmp = x - (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+59) || !(z <= 6.4e-9)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.5e+59) or not (z <= 6.4e-9):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e+59) || !(z <= 6.4e-9))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.5e+59) || ~((z <= 6.4e-9)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e+59], N[Not[LessEqual[z, 6.4e-9]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e59 or 6.40000000000000023e-9 < z

   1. Initial program 93.4%

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

   5. Taylor expanded in z around inf 82.1%

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

   if -3.5e59 < z < 6.40000000000000023e-9

   1. Initial program 99.9%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 89.8%

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

      1. associate-/l* 91.7%

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

   7. Simplified 91.7%

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

   8. Taylor expanded in t around 0 77.4%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+59} \lor \neg \left(z \leq 6.4 \cdot 10^{-9}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+34} \lor \neg \left(z \leq 1.05 \cdot 10^{-9}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.2e+34) (not (<= z 1.05e-9))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.2e+34) || !(z <= 1.05e-9)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.2d+34)) .or. (.not. (z <= 1.05d-9))) then
        tmp = x - a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.2e+34) || !(z <= 1.05e-9)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.2e+34) or not (z <= 1.05e-9):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.2e+34) || !(z <= 1.05e-9))
		tmp = Float64(x - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.2e+34) || ~((z <= 1.05e-9)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.2e+34], N[Not[LessEqual[z, 1.05e-9]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.1999999999999997e34 or 1.0500000000000001e-9 < z

   1. Initial program 93.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 81.5%

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

   if -8.1999999999999997e34 < z < 1.0500000000000001e-9

   1. Initial program 99.9%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 90.6%

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

      1. associate-/l* 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in x around inf 65.3%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+34} \lor \neg \left(z \leq 1.05 \cdot 10^{-9}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.9% 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 97.1%

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

   1. associate-/r/ 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in z around 0 69.9%

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

   1. associate-/l* 71.3%

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

7. Simplified 71.3%

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

8. Taylor expanded in x around inf 56.7%

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

9. Final simplification 56.7%

   \[\leadsto x \]
10. Add Preprocessing

Developer target: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024036 
(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))))