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

Percentage Accurate: 97.1% → 99.6%

Time: 12.1s

Alternatives: 10

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: 97.1% 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

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

FPCore

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

C

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

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 / (((t - z) + 1.0d0) / (z - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

   1. associate-/r/ 99.8%

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

3. Simplified 99.8%

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

   1. *-commutative 99.8%

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

   2. clear-num 99.8%

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

   3. un-div-inv 99.9%

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

6. Applied egg-rr 99.9%

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

7. Final simplification 99.9%

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

Alternative 2: 92.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -26 \lor \neg \left(z \leq 2.7 \cdot 10^{+47}\right):\\ \;\;\;\;x - a \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -26.0) (not (<= z 2.7e+47)))
   (- x (* a (/ (- z y) z)))
   (+ x (/ (- y z) (/ (- -1.0 t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -26.0) || !(z <= 2.7e+47)) {
		tmp = x - (a * ((z - y) / z));
	} else {
		tmp = x + ((y - z) / ((-1.0 - t) / 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 <= (-26.0d0)) .or. (.not. (z <= 2.7d+47))) then
        tmp = x - (a * ((z - y) / z))
    else
        tmp = x + ((y - z) / (((-1.0d0) - t) / 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 <= -26.0) || !(z <= 2.7e+47)) {
		tmp = x - (a * ((z - y) / z));
	} else {
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -26.0) or not (z <= 2.7e+47):
		tmp = x - (a * ((z - y) / z))
	else:
		tmp = x + ((y - z) / ((-1.0 - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -26.0) || !(z <= 2.7e+47))
		tmp = Float64(x - Float64(a * Float64(Float64(z - y) / z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(-1.0 - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -26.0) || ~((z <= 2.7e+47)))
		tmp = x - (a * ((z - y) / z));
	else
		tmp = x + ((y - z) / ((-1.0 - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -26.0], N[Not[LessEqual[z, 2.7e+47]], $MachinePrecision]], N[(x - N[(a * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(-1.0 - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -26 or 2.69999999999999996e47 < 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/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 92.7%

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

      1. mul-1-neg 92.7%

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

   7. Simplified 92.7%

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

   if -26 < z < 2.69999999999999996e47

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 98.6%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -26 \lor \neg \left(z \leq 2.7 \cdot 10^{+47}\right):\\ \;\;\;\;x - a \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{-1 - t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10.5 \lor \neg \left(z \leq 2.7 \cdot 10^{+47}\right):\\ \;\;\;\;x - a \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{-1 - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -10.5) (not (<= z 2.7e+47)))
   (- x (* a (/ (- z y) z)))
   (+ x (/ a (/ (- -1.0 t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -10.5) || !(z <= 2.7e+47)) {
		tmp = x - (a * ((z - y) / z));
	} else {
		tmp = x + (a / ((-1.0 - t) / 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 <= (-10.5d0)) .or. (.not. (z <= 2.7d+47))) then
        tmp = x - (a * ((z - y) / z))
    else
        tmp = x + (a / (((-1.0d0) - t) / 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 <= -10.5) || !(z <= 2.7e+47)) {
		tmp = x - (a * ((z - y) / z));
	} else {
		tmp = x + (a / ((-1.0 - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -10.5) or not (z <= 2.7e+47):
		tmp = x - (a * ((z - y) / z))
	else:
		tmp = x + (a / ((-1.0 - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -10.5) || !(z <= 2.7e+47))
		tmp = Float64(x - Float64(a * Float64(Float64(z - y) / z)));
	else
		tmp = Float64(x + Float64(a / Float64(Float64(-1.0 - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -10.5) || ~((z <= 2.7e+47)))
		tmp = x - (a * ((z - y) / z));
	else
		tmp = x + (a / ((-1.0 - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -10.5], N[Not[LessEqual[z, 2.7e+47]], $MachinePrecision]], N[(x - N[(a * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a / N[(N[(-1.0 - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -10.5 or 2.69999999999999996e47 < 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/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 92.7%

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

      1. mul-1-neg 92.7%

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

   7. Simplified 92.7%

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

   if -10.5 < z < 2.69999999999999996e47

   1. Initial program 99.6%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around 0 92.6%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10.5 \lor \neg \left(z \leq 2.7 \cdot 10^{+47}\right):\\ \;\;\;\;x - a \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{-1 - t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -18500000 \lor \neg \left(z \leq 2.7 \cdot 10^{+47}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{-1 - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -18500000.0) (not (<= z 2.7e+47)))
   (- x a)
   (+ x (/ a (/ (- -1.0 t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -18500000.0) || !(z <= 2.7e+47)) {
		tmp = x - a;
	} else {
		tmp = x + (a / ((-1.0 - t) / 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 <= (-18500000.0d0)) .or. (.not. (z <= 2.7d+47))) then
        tmp = x - a
    else
        tmp = x + (a / (((-1.0d0) - t) / 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 <= -18500000.0) || !(z <= 2.7e+47)) {
		tmp = x - a;
	} else {
		tmp = x + (a / ((-1.0 - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -18500000.0) or not (z <= 2.7e+47):
		tmp = x - a
	else:
		tmp = x + (a / ((-1.0 - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -18500000.0) || !(z <= 2.7e+47))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a / Float64(Float64(-1.0 - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -18500000.0) || ~((z <= 2.7e+47)))
		tmp = x - a;
	else
		tmp = x + (a / ((-1.0 - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -18500000.0], N[Not[LessEqual[z, 2.7e+47]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a / N[(N[(-1.0 - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e7 or 2.69999999999999996e47 < 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/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 81.1%

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

   if -1.85e7 < z < 2.69999999999999996e47

   1. Initial program 99.6%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around 0 92.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -18500000 \lor \neg \left(z \leq 2.7 \cdot 10^{+47}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{-1 - t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -70000000 \lor \neg \left(z \leq 8 \cdot 10^{+47}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -70000000.0) (not (<= z 8e+47)))
   (- x a)
   (+ x (* a (/ (- z y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -70000000.0) || !(z <= 8e+47)) {
		tmp = x - a;
	} else {
		tmp = x + (a * ((z - y) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-70000000.0d0)) .or. (.not. (z <= 8d+47))) then
        tmp = x - a
    else
        tmp = x + (a * ((z - y) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -70000000.0) || !(z <= 8e+47)) {
		tmp = x - a;
	} else {
		tmp = x + (a * ((z - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -70000000.0) or not (z <= 8e+47):
		tmp = x - a
	else:
		tmp = x + (a * ((z - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -70000000.0) || !(z <= 8e+47))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -70000000.0) || ~((z <= 8e+47)))
		tmp = x - a;
	else
		tmp = x + (a * ((z - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -70000000.0], N[Not[LessEqual[z, 8e+47]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7e7 or 8.0000000000000004e47 < 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/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 81.1%

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

   if -7e7 < z < 8.0000000000000004e47

   1. Initial program 99.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 65.3%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -70000000 \lor \neg \left(z \leq 8 \cdot 10^{+47}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -11200000 \lor \neg \left(z \leq 3 \cdot 10^{+47}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -11200000.0) (not (<= z 3e+47))) (- x a) (- x (* a (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -11200000.0) || !(z <= 3e+47)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-11200000.0d0)) .or. (.not. (z <= 3d+47))) then
        tmp = x - a
    else
        tmp = x - (a * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -11200000.0) || !(z <= 3e+47)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -11200000.0) or not (z <= 3e+47):
		tmp = x - a
	else:
		tmp = x - (a * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -11200000.0) || !(z <= 3e+47))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -11200000.0) || ~((z <= 3e+47)))
		tmp = x - a;
	else
		tmp = x - (a * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -11200000.0], N[Not[LessEqual[z, 3e+47]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12e7 or 3.0000000000000001e47 < 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/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 81.1%

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

   if -1.12e7 < z < 3.0000000000000001e47

   1. Initial program 99.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 60.6%

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

   6. Taylor expanded in y around inf 60.6%

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

      1. associate-/l* 64.6%

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

   8. Simplified 64.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -11200000 \lor \neg \left(z \leq 3 \cdot 10^{+47}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -21 \lor \neg \left(z \leq 1.95 \cdot 10^{+49}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -21.0) (not (<= z 1.95e+49))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -21.0) || !(z <= 1.95e+49)) {
		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 <= (-21.0d0)) .or. (.not. (z <= 1.95d+49))) 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 <= -21.0) || !(z <= 1.95e+49)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -21.0) or not (z <= 1.95e+49):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -21.0) || !(z <= 1.95e+49))
		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 <= -21.0) || ~((z <= 1.95e+49)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -21.0], N[Not[LessEqual[z, 1.95e+49]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -21 or 1.95e49 < 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/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 80.7%

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

   if -21 < z < 1.95e49

   1. Initial program 99.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 x around inf 52.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -21 \lor \neg \left(z \leq 1.95 \cdot 10^{+49}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

   1. associate-/r/ 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 9: 54.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-263}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.6e-68) x (if (<= x 6e-263) (- a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.6e-68) {
		tmp = x;
	} else if (x <= 6e-263) {
		tmp = -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 (x <= (-2.6d-68)) then
        tmp = x
    else if (x <= 6d-263) then
        tmp = -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 (x <= -2.6e-68) {
		tmp = x;
	} else if (x <= 6e-263) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.6e-68:
		tmp = x
	elif x <= 6e-263:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.6e-68)
		tmp = x;
	elseif (x <= 6e-263)
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.6e-68)
		tmp = x;
	elseif (x <= 6e-263)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.6e-68], x, If[LessEqual[x, 6e-263], (-a), x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999998e-68 or 6.0000000000000001e-263 < x

   1. Initial program 99.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 x around inf 60.1%

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

   if -2.5999999999999998e-68 < x < 6.0000000000000001e-263

   1. Initial program 93.2%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 62.7%

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

      1. mul-1-neg 62.7%

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

      2. associate--l+ 62.7%

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

      3. +-commutative 62.7%

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

      4. associate-*l/ 78.8%

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

      5. *-commutative 78.8%

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

      6. distribute-rgt-neg-out 78.8%

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

      7. distribute-neg-frac2 78.8%

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

      8. associate-+l- 78.8%

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

      9. sub-neg 78.8%

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

      10. metadata-eval 78.8%

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

      11. +-commutative 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in z around inf 41.5%

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

      1. neg-mul-1 41.5%

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

   10. Simplified 41.5%

       \[\leadsto \color{blue}{-a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 54.4% 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 97.8%

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

   1. associate-/r/ 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around inf 49.2%

   \[\leadsto \color{blue}{x} \]
6. 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 2024087 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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