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

Percentage Accurate: 97.0% → 99.7%

Time: 12.3s

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: 97.0% 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

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

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 95.5%

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

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

Alternative 2: 82.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+101}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-76}:\\ \;\;\;\;x + a \cdot \frac{z}{t + 1}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+88}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.7e+101)
   (- x a)
   (if (<= z -1.18e-76)
     (+ x (* a (/ z (+ t 1.0))))
     (if (<= z 1.32e+88) (+ x (* a (/ y (- -1.0 t)))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e+101) {
		tmp = x - a;
	} else if (z <= -1.18e-76) {
		tmp = x + (a * (z / (t + 1.0)));
	} else if (z <= 1.32e+88) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.7d+101)) then
        tmp = x - a
    else if (z <= (-1.18d-76)) then
        tmp = x + (a * (z / (t + 1.0d0)))
    else if (z <= 1.32d+88) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.7e+101) {
		tmp = x - a;
	} else if (z <= -1.18e-76) {
		tmp = x + (a * (z / (t + 1.0)));
	} else if (z <= 1.32e+88) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.7e+101:
		tmp = x - a
	elif z <= -1.18e-76:
		tmp = x + (a * (z / (t + 1.0)))
	elif z <= 1.32e+88:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.7e+101)
		tmp = Float64(x - a);
	elseif (z <= -1.18e-76)
		tmp = Float64(x + Float64(a * Float64(z / Float64(t + 1.0))));
	elseif (z <= 1.32e+88)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.7e+101)
		tmp = x - a;
	elseif (z <= -1.18e-76)
		tmp = x + (a * (z / (t + 1.0)));
	elseif (z <= 1.32e+88)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.7e+101], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.18e-76], N[(x + N[(a * N[(z / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.32e+88], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.69999999999999971e101 or 1.3200000000000001e88 < z

   1. Initial program 92.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 86.8%

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

   if -4.69999999999999971e101 < z < -1.17999999999999993e-76

   1. Initial program 94.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 86.2%

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

      1. associate--l+ 86.2%

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

      2. +-commutative 86.2%

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

      3. neg-mul-1 86.2%

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

      4. distribute-neg-frac2 86.2%

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

      5. +-commutative 86.2%

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

      6. distribute-neg-in 86.2%

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

      7. metadata-eval 86.2%

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

      8. unsub-neg 86.2%

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

   7. Simplified 86.2%

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

   8. Taylor expanded in z around 0 76.4%

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

      1. distribute-lft-in 76.4%

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

      2. metadata-eval 76.4%

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

      3. neg-mul-1 76.4%

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

      4. sub-neg 76.4%

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

   10. Simplified 76.4%

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

   if -1.17999999999999993e-76 < z < 1.3200000000000001e88

   1. Initial program 97.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around 0 86.3%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+101}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-76}:\\ \;\;\;\;x + a \cdot \frac{z}{t + 1}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+88}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+16} \lor \neg \left(t \leq 1.2\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.2e+16) (not (<= t 1.2)))
   (+ x (* a (/ z (+ (- t z) 1.0))))
   (+ x (* a (/ (- y z) (+ z -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.2e+16) || !(t <= 1.2)) {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	} else {
		tmp = x + (a * ((y - z) / (z + -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 ((t <= (-6.2d+16)) .or. (.not. (t <= 1.2d0))) then
        tmp = x + (a * (z / ((t - z) + 1.0d0)))
    else
        tmp = x + (a * ((y - z) / (z + (-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 ((t <= -6.2e+16) || !(t <= 1.2)) {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	} else {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.2e+16) or not (t <= 1.2):
		tmp = x + (a * (z / ((t - z) + 1.0)))
	else:
		tmp = x + (a * ((y - z) / (z + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.2e+16) || !(t <= 1.2))
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(t - z) + 1.0))));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / Float64(z + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.2e+16) || ~((t <= 1.2)))
		tmp = x + (a * (z / ((t - z) + 1.0)));
	else
		tmp = x + (a * ((y - z) / (z + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.2e+16], N[Not[LessEqual[t, 1.2]], $MachinePrecision]], N[(x + N[(a * N[(z / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2e16 or 1.19999999999999996 < t

   1. Initial program 94.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 y around 0 84.1%

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

      1. associate--l+ 84.1%

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

      2. +-commutative 84.1%

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

      3. neg-mul-1 84.1%

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

      4. distribute-neg-frac2 84.1%

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

      5. +-commutative 84.1%

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

      6. distribute-neg-in 84.1%

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

      7. metadata-eval 84.1%

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

      8. unsub-neg 84.1%

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

   7. Simplified 84.1%

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

   if -6.2e16 < t < 1.19999999999999996

   1. Initial program 96.0%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 99.4%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+16} \lor \neg \left(t \leq 1.2\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-76} \lor \neg \left(z \leq 8.5 \cdot 10^{-27}\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.25e-76) (not (<= z 8.5e-27)))
   (+ x (* a (/ z (+ (- t z) 1.0))))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e-76) || !(z <= 8.5e-27)) {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	} else {
		tmp = x + (a * (y / (-1.0 - 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 <= (-1.25d-76)) .or. (.not. (z <= 8.5d-27))) then
        tmp = x + (a * (z / ((t - z) + 1.0d0)))
    else
        tmp = x + (a * (y / ((-1.0d0) - 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 <= -1.25e-76) || !(z <= 8.5e-27)) {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.25e-76) or not (z <= 8.5e-27):
		tmp = x + (a * (z / ((t - z) + 1.0)))
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.25e-76) || !(z <= 8.5e-27))
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(t - z) + 1.0))));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.25e-76) || ~((z <= 8.5e-27)))
		tmp = x + (a * (z / ((t - z) + 1.0)));
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.25e-76], N[Not[LessEqual[z, 8.5e-27]], $MachinePrecision]], N[(x + N[(a * N[(z / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2499999999999999e-76 or 8.50000000000000033e-27 < z

   1. Initial program 93.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 88.1%

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

      1. associate--l+ 88.1%

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

      2. +-commutative 88.1%

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

      3. neg-mul-1 88.1%

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

      4. distribute-neg-frac2 88.1%

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

      5. +-commutative 88.1%

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

      6. distribute-neg-in 88.1%

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

      7. metadata-eval 88.1%

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

      8. unsub-neg 88.1%

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

   7. Simplified 88.1%

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

   if -1.2499999999999999e-76 < z < 8.50000000000000033e-27

   1. Initial program 98.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 95.1%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-76} \lor \neg \left(z \leq 8.5 \cdot 10^{-27}\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-15} \lor \neg \left(z \leq 2.6 \cdot 10^{+21}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.15e-15) (not (<= z 2.6e+21)))
   (+ x (* (- y z) (/ a z)))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.15e-15) || !(z <= 2.6e+21)) {
		tmp = x + ((y - z) * (a / z));
	} else {
		tmp = x + (a * (y / (-1.0 - 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 <= (-2.15d-15)) .or. (.not. (z <= 2.6d+21))) then
        tmp = x + ((y - z) * (a / z))
    else
        tmp = x + (a * (y / ((-1.0d0) - 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 <= -2.15e-15) || !(z <= 2.6e+21)) {
		tmp = x + ((y - z) * (a / z));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.15e-15) or not (z <= 2.6e+21):
		tmp = x + ((y - z) * (a / z))
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.15e-15) || !(z <= 2.6e+21))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(a / z)));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.15e-15) || ~((z <= 2.6e+21)))
		tmp = x + ((y - z) * (a / z));
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.15e-15], N[Not[LessEqual[z, 2.6e+21]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1499999999999998e-15 or 2.6e21 < z

   1. Initial program 92.9%

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

      1. clear-num 92.8%

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

      2. associate-/r/ 92.8%

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

      3. clear-num 94.4%

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

   4. Applied egg-rr 94.4%

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

   5. Taylor expanded in z around inf 82.8%

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

      1. associate-*r/ 82.8%

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

      2. neg-mul-1 82.8%

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

   7. Simplified 82.8%

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

   if -2.1499999999999998e-15 < z < 2.6e21

   1. Initial program 98.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around 0 89.9%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-15} \lor \neg \left(z \leq 2.6 \cdot 10^{+21}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-15} \lor \neg \left(z \leq 1.18 \cdot 10^{+88}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.15e-15) (not (<= z 1.18e+88)))
   (- x a)
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.15e-15) || !(z <= 1.18e+88)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - 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 <= (-2.15d-15)) .or. (.not. (z <= 1.18d+88))) then
        tmp = x - a
    else
        tmp = x + (a * (y / ((-1.0d0) - 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 <= -2.15e-15) || !(z <= 1.18e+88)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.15e-15) or not (z <= 1.18e+88):
		tmp = x - a
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.15e-15) || !(z <= 1.18e+88))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.15e-15) || ~((z <= 1.18e+88)))
		tmp = x - a;
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.15e-15], N[Not[LessEqual[z, 1.18e+88]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1499999999999998e-15 or 1.1799999999999999e88 < z

   1. Initial program 93.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 82.0%

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

   if -2.1499999999999998e-15 < z < 1.1799999999999999e88

   1. Initial program 97.2%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 84.5%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-15} \lor \neg \left(z \leq 1.18 \cdot 10^{+88}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-100} \lor \neg \left(z \leq 0.22\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.75e-100) (not (<= z 0.22))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.75e-100) || !(z <= 0.22)) {
		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 <= (-1.75d-100)) .or. (.not. (z <= 0.22d0))) 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 <= -1.75e-100) || !(z <= 0.22)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.75e-100) or not (z <= 0.22):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.75e-100) || !(z <= 0.22))
		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 <= -1.75e-100) || ~((z <= 0.22)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.75e-100], N[Not[LessEqual[z, 0.22]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e-100 or 0.220000000000000001 < 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 75.0%

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

   if -1.75e-100 < z < 0.220000000000000001

   1. Initial program 98.9%

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

      1. *-commutative 99.0%

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

      2. clear-num 98.9%

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

      3. un-div-inv 98.9%

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

   6. Applied egg-rr 98.9%

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

   7. Taylor expanded in t around 0 78.5%

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

   8. Taylor expanded in z around 0 73.8%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-100} \lor \neg \left(z \leq 0.22\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-15} \lor \neg \left(z \leq 2.6 \cdot 10^{+21}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e-15) (not (<= z 2.6e+21))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e-15) || !(z <= 2.6e+21)) {
		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 <= (-1.6d-15)) .or. (.not. (z <= 2.6d+21))) 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 <= -1.6e-15) || !(z <= 2.6e+21)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.6e-15) or not (z <= 2.6e+21):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.6e-15) || !(z <= 2.6e+21))
		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 <= -1.6e-15) || ~((z <= 2.6e+21)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.6e-15], N[Not[LessEqual[z, 2.6e+21]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e-15 or 2.6e21 < z

   1. Initial program 92.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 77.2%

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

   if -1.6e-15 < z < 2.6e21

   1. Initial program 98.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 45.4%

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

   6. Taylor expanded in x around inf 57.4%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-15} \lor \neg \left(z \leq 2.6 \cdot 10^{+21}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * (a / (-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 + ((y - z) * (a / ((-1.0d0) + (z - t))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

   1. clear-num 95.4%

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

   2. associate-/r/ 95.5%

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

   3. clear-num 96.3%

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

4. Applied egg-rr 96.3%

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

5. Final simplification 96.3%

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

Alternative 10: 53.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+125}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a -2.1e+125) (- a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e+125) {
		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 (a <= (-2.1d+125)) 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 (a <= -2.1e+125) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.1e+125:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e+125)
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.1e+125)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e+125], (-a), x]

Derivation

1. Split input into 2 regimes

2. if a < -2.1000000000000001e125

   1. Initial program 99.5%

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

      1. associate-/r/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around inf 34.8%

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

   6. Taylor expanded in x around 0 30.9%

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

      1. neg-mul-1 30.9%

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

   8. Simplified 30.9%

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

   if -2.1000000000000001e125 < a

   1. Initial program 94.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 66.1%

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

   6. Taylor expanded in x around inf 59.6%

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

Alternative 11: 53.3% 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 95.5%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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 inf 61.9%

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

6. Taylor expanded in x around inf 53.3%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Developer Target 1: 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 2024145 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (/ (- y z) (+ (- t z) 1)) a)))

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