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

Percentage Accurate: 97.2% → 99.6%

Time: 7.0s

Alternatives: 8

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: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

   1. associate-/r/ 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 89.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1900 \lor \neg \left(z \leq 1.65 \cdot 10^{-25}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1900.0) (not (<= z 1.65e-25)))
   (+ x (* a (/ (- z y) (- 1.0 z))))
   (- x (/ a (/ (+ t 1.0) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1900.0) || !(z <= 1.65e-25)) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} 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 <= (-1900.0d0)) .or. (.not. (z <= 1.65d-25))) then
        tmp = x + (a * ((z - y) / (1.0d0 - z)))
    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 <= -1900.0) || !(z <= 1.65e-25)) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else {
		tmp = x - (a / ((t + 1.0) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1900.0) or not (z <= 1.65e-25):
		tmp = x + (a * ((z - y) / (1.0 - z)))
	else:
		tmp = x - (a / ((t + 1.0) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1900.0) || !(z <= 1.65e-25))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(1.0 - z))));
	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 <= -1900.0) || ~((z <= 1.65e-25)))
		tmp = x + (a * ((z - y) / (1.0 - z)));
	else
		tmp = x - (a / ((t + 1.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1900.0], N[Not[LessEqual[z, 1.65e-25]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $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 < -1900 or 1.6499999999999999e-25 < 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. Taylor expanded in t around 0 89.5%

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

   if -1900 < z < 1.6499999999999999e-25

   1. Initial program 99.1%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around 0 95.3%

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

      1. associate-/l* 97.6%

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

   6. Simplified 97.6%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1900 \lor \neg \left(z \leq 1.65 \cdot 10^{-25}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \]

Alternative 3: 87.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4500 \lor \neg \left(z \leq 2.65 \cdot 10^{-6}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4500.0) (not (<= z 2.65e-6)))
   (+ 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 <= -4500.0) || !(z <= 2.65e-6)) {
		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 <= (-4500.0d0)) .or. (.not. (z <= 2.65d-6))) 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 <= -4500.0) || !(z <= 2.65e-6)) {
		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 <= -4500.0) or not (z <= 2.65e-6):
		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 <= -4500.0) || !(z <= 2.65e-6))
		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 <= -4500.0) || ~((z <= 2.65e-6)))
		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, -4500.0], N[Not[LessEqual[z, 2.65e-6]], $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 < -4500 or 2.65e-6 < z

   1. Initial program 93.1%

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

   2. Taylor expanded in z around inf 82.3%

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

      1. mul-1-neg 82.3%

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

      2. distribute-neg-frac 82.3%

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

   4. Simplified 82.3%

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

   if -4500 < z < 2.65e-6

   1. Initial program 99.1%

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

      1. associate-/r/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around 0 95.4%

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

      1. associate-/l* 97.6%

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

   6. Simplified 97.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4500 \lor \neg \left(z \leq 2.65 \cdot 10^{-6}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \end{array} \]

Alternative 4: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -500000000000:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+17}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -500000000000.0)
   (- x (+ a (/ a z)))
   (if (<= z 8.8e+17) (- 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 <= -500000000000.0) {
		tmp = x - (a + (a / z));
	} else if (z <= 8.8e+17) {
		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 <= (-500000000000.0d0)) then
        tmp = x - (a + (a / z))
    else if (z <= 8.8d+17) 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 <= -500000000000.0) {
		tmp = x - (a + (a / z));
	} else if (z <= 8.8e+17) {
		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 <= -500000000000.0:
		tmp = x - (a + (a / z))
	elif z <= 8.8e+17:
		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 <= -500000000000.0)
		tmp = Float64(x - Float64(a + Float64(a / z)));
	elseif (z <= 8.8e+17)
		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 <= -500000000000.0)
		tmp = x - (a + (a / z));
	elseif (z <= 8.8e+17)
		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, -500000000000.0], N[(x - N[(a + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+17], N[(x - N[(a / N[(N[(t + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5e11

   1. Initial program 93.2%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 89.8%

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

   5. Taylor expanded in y around 0 82.7%

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

      1. neg-mul-1 82.7%

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

      2. distribute-neg-frac 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in z around inf 82.7%

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

   if -5e11 < z < 8.8e17

   1. Initial program 99.1%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in z around 0 93.5%

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

      1. associate-/l* 95.6%

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

   6. Simplified 95.6%

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

   if 8.8e17 < z

   1. Initial program 91.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.1%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -500000000000:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+17}:\\ \;\;\;\;x - \frac{a}{\frac{t + 1}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 5: 73.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -490000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 62000000000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -490000000000.0)
   (- x a)
   (if (<= z 62000000000.0) (- x (* y a)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -490000000000.0) {
		tmp = x - a;
	} else if (z <= 62000000000.0) {
		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 <= (-490000000000.0d0)) then
        tmp = x - a
    else if (z <= 62000000000.0d0) 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 <= -490000000000.0) {
		tmp = x - a;
	} else if (z <= 62000000000.0) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -490000000000.0:
		tmp = x - a
	elif z <= 62000000000.0:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -490000000000.0)
		tmp = Float64(x - a);
	elseif (z <= 62000000000.0)
		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 <= -490000000000.0)
		tmp = x - a;
	elseif (z <= 62000000000.0)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -490000000000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 62000000000.0], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9e11 or 6.2e10 < z

   1. Initial program 92.6%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.0%

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

   if -4.9e11 < z < 6.2e10

   1. Initial program 99.1%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in t around 0 79.6%

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

   5. Taylor expanded in z around 0 79.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -490000000000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 62000000000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 6: 73.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -290000000000:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+16}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -290000000000.0)
   (- x (+ a (/ a z)))
   (if (<= z 7e+16) (- x (* y a)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -290000000000.0) {
		tmp = x - (a + (a / z));
	} else if (z <= 7e+16) {
		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 <= (-290000000000.0d0)) then
        tmp = x - (a + (a / z))
    else if (z <= 7d+16) 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 <= -290000000000.0) {
		tmp = x - (a + (a / z));
	} else if (z <= 7e+16) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -290000000000.0:
		tmp = x - (a + (a / z))
	elif z <= 7e+16:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -290000000000.0)
		tmp = Float64(x - Float64(a + Float64(a / z)));
	elseif (z <= 7e+16)
		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 <= -290000000000.0)
		tmp = x - (a + (a / z));
	elseif (z <= 7e+16)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -290000000000.0], N[(x - N[(a + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+16], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e11

   1. Initial program 93.2%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 89.8%

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

   5. Taylor expanded in y around 0 82.7%

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

      1. neg-mul-1 82.7%

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

      2. distribute-neg-frac 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in z around inf 82.7%

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

   if -2.9e11 < z < 7e16

   1. Initial program 99.1%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in t around 0 79.6%

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

   5. Taylor expanded in z around 0 79.1%

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

   if 7e16 < z

   1. Initial program 91.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 77.1%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -290000000000:\\ \;\;\;\;x - \left(a + \frac{a}{z}\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+16}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 7: 66.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e+14) (- x a) (if (<= z 2.4e+16) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+14) {
		tmp = x - a;
	} else if (z <= 2.4e+16) {
		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 <= (-2.8d+14)) then
        tmp = x - a
    else if (z <= 2.4d+16) 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 <= -2.8e+14) {
		tmp = x - a;
	} else if (z <= 2.4e+16) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e+14:
		tmp = x - a
	elif z <= 2.4e+16:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e+14)
		tmp = Float64(x - a);
	elseif (z <= 2.4e+16)
		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 <= -2.8e+14)
		tmp = x - a;
	elseif (z <= 2.4e+16)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e+14], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.4e+16], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e14 or 2.4e16 < z

   1. Initial program 92.6%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 80.1%

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

   if -2.8e14 < z < 2.4e16

   1. Initial program 99.1%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in x around inf 63.4%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 8: 53.8% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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. Taylor expanded in x around inf 55.5%

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

5. Final simplification 55.5%

   \[\leadsto x \]

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 2023196 
(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))))