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

Percentage Accurate: 97.0% → 99.8%

Time: 9.0s

Alternatives: 9

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: 99.8% 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 94.2%

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

   1. associate-/r/ 99.9%

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

   2. *-commutative 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 87.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+35}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+203}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ a z)))))
   (if (<= z -3.6e+25)
     t_1
     (if (<= z 5.4e+35)
       (- x (* a (/ y (+ t 1.0))))
       (if (<= z 5.2e+203) t_1 (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (a / z));
	double tmp;
	if (z <= -3.6e+25) {
		tmp = t_1;
	} else if (z <= 5.4e+35) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 5.2e+203) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * (a / z))
    if (z <= (-3.6d+25)) then
        tmp = t_1
    else if (z <= 5.4d+35) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else if (z <= 5.2d+203) then
        tmp = t_1
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (a / z));
	double tmp;
	if (z <= -3.6e+25) {
		tmp = t_1;
	} else if (z <= 5.4e+35) {
		tmp = x - (a * (y / (t + 1.0)));
	} else if (z <= 5.2e+203) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (a / z))
	tmp = 0
	if z <= -3.6e+25:
		tmp = t_1
	elif z <= 5.4e+35:
		tmp = x - (a * (y / (t + 1.0)))
	elif z <= 5.2e+203:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(a / z)))
	tmp = 0.0
	if (z <= -3.6e+25)
		tmp = t_1;
	elseif (z <= 5.4e+35)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	elseif (z <= 5.2e+203)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (a / z));
	tmp = 0.0;
	if (z <= -3.6e+25)
		tmp = t_1;
	elseif (z <= 5.4e+35)
		tmp = x - (a * (y / (t + 1.0)));
	elseif (z <= 5.2e+203)
		tmp = t_1;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+25], t$95$1, If[LessEqual[z, 5.4e+35], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+203], t$95$1, N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.60000000000000015e25 or 5.40000000000000005e35 < z < 5.1999999999999997e203

   1. Initial program 91.4%

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

      1. clear-num 91.3%

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

      2. associate-/r/ 91.4%

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

      3. clear-num 94.4%

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

   3. Applied egg-rr 94.4%

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

   4. Taylor expanded in z around inf 83.1%

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

      1. associate-*r/ 83.1%

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

      2. mul-1-neg 83.1%

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

   6. Simplified 83.1%

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

   if -3.60000000000000015e25 < z < 5.40000000000000005e35

   1. Initial program 99.2%

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

      1. associate-/r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 94.2%

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

   if 5.1999999999999997e203 < z

   1. Initial program 75.3%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 96.1%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+25}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+35}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+203}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 3: 88.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+70} \lor \neg \left(z \leq 5 \cdot 10^{-27}\right):\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.18e+70) (not (<= z 5e-27)))
   (+ x (/ a (/ (+ (- t z) 1.0) z)))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.18e+70) || !(z <= 5e-27)) {
		tmp = x + (a / (((t - z) + 1.0) / z));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.18d+70)) .or. (.not. (z <= 5d-27))) then
        tmp = x + (a / (((t - z) + 1.0d0) / z))
    else
        tmp = x - (a * (y / (t + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.18e+70) || !(z <= 5e-27)) {
		tmp = x + (a / (((t - z) + 1.0) / z));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.18e+70) or not (z <= 5e-27):
		tmp = x + (a / (((t - z) + 1.0) / z))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.18e+70) || !(z <= 5e-27))
		tmp = Float64(x + Float64(a / Float64(Float64(Float64(t - z) + 1.0) / z)));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.18e+70) || ~((z <= 5e-27)))
		tmp = x + (a / (((t - z) + 1.0) / z));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.18e+70], N[Not[LessEqual[z, 5e-27]], $MachinePrecision]], N[(x + N[(a / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.18000000000000001e70 or 5.0000000000000002e-27 < z

   1. Initial program 88.7%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 66.3%

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

      1. mul-1-neg 66.3%

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

      2. *-commutative 66.3%

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

      3. associate--l+ 66.3%

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

      4. +-commutative 66.3%

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

      5. associate-*l/ 87.9%

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

      6. distribute-lft-neg-in 87.9%

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

      7. distribute-neg-frac 87.9%

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

      8. +-commutative 87.9%

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

   6. Simplified 87.9%

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

   7. Taylor expanded in x around 0 66.3%

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

      1. +-commutative 66.3%

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

      2. associate-/l* 87.8%

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

      3. associate--l+ 87.8%

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

   9. Simplified 87.8%

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

   if -1.18000000000000001e70 < z < 5.0000000000000002e-27

   1. Initial program 99.1%

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

      1. associate-/r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 95.6%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+70} \lor \neg \left(z \leq 5 \cdot 10^{-27}\right):\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]

Alternative 4: 91.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+95} \lor \neg \left(t \leq 5.6 \cdot 10^{+125}\right):\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.22e+95) (not (<= t 5.6e+125)))
   (- x (* a (/ (- y z) t)))
   (- x (* a (/ (- y z) (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.22e+95) || !(t <= 5.6e+125)) {
		tmp = x - (a * ((y - z) / t));
	} else {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.22d+95)) .or. (.not. (t <= 5.6d+125))) then
        tmp = x - (a * ((y - z) / t))
    else
        tmp = x - (a * ((y - z) / (1.0d0 - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.22e+95) || !(t <= 5.6e+125)) {
		tmp = x - (a * ((y - z) / t));
	} else {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.22e+95) or not (t <= 5.6e+125):
		tmp = x - (a * ((y - z) / t))
	else:
		tmp = x - (a * ((y - z) / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.22e+95) || !(t <= 5.6e+125))
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / t)));
	else
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.22e+95) || ~((t <= 5.6e+125)))
		tmp = x - (a * ((y - z) / t));
	else
		tmp = x - (a * ((y - z) / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.22e+95], N[Not[LessEqual[t, 5.6e+125]], $MachinePrecision]], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.22000000000000007e95 or 5.6000000000000002e125 < t

   1. Initial program 93.0%

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

      1. associate-/r/ 99.6%

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

      2. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 92.3%

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

   if -1.22000000000000007e95 < t < 5.6000000000000002e125

   1. Initial program 94.7%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 96.5%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+95} \lor \neg \left(t \leq 5.6 \cdot 10^{+125}\right):\\ \;\;\;\;x - a \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \end{array} \]

Alternative 5: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+109} \lor \neg \left(z \leq 2.4\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e+109) (not (<= z 2.4)))
   (- x a)
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+109) || !(z <= 2.4)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.15d+109)) .or. (.not. (z <= 2.4d0))) then
        tmp = x - a
    else
        tmp = x - (a * (y / (t + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+109) || !(z <= 2.4)) {
		tmp = x - a;
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e+109) or not (z <= 2.4):
		tmp = x - a
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e+109) || !(z <= 2.4))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.15e+109) || ~((z <= 2.4)))
		tmp = x - a;
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e+109], N[Not[LessEqual[z, 2.4]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000005e109 or 2.39999999999999991 < z

   1. Initial program 88.1%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 79.6%

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

   if -1.15000000000000005e109 < z < 2.39999999999999991

   1. Initial program 98.6%

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

      1. associate-/r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 92.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+109} \lor \neg \left(z \leq 2.4\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]

Alternative 6: 73.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-40}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-24}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e-40) (- x a) (if (<= z 9.8e-24) (- x (* a y)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e-40) {
		tmp = x - a;
	} else if (z <= 9.8e-24) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.4d-40)) then
        tmp = x - a
    else if (z <= 9.8d-24) then
        tmp = x - (a * y)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e-40) {
		tmp = x - a;
	} else if (z <= 9.8e-24) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e-40:
		tmp = x - a
	elif z <= 9.8e-24:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e-40)
		tmp = Float64(x - a);
	elseif (z <= 9.8e-24)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.4e-40)
		tmp = x - a;
	elseif (z <= 9.8e-24)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e-40], N[(x - a), $MachinePrecision], If[LessEqual[z, 9.8e-24], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000018e-40 or 9.8000000000000002e-24 < z

   1. Initial program 89.5%

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

      1. associate-/r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 75.0%

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

   if -4.40000000000000018e-40 < z < 9.8000000000000002e-24

   1. Initial program 99.9%

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

      1. associate-/r/ 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 95.0%

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

      1. associate-/l* 98.2%

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

   6. Simplified 98.2%

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

   7. Taylor expanded in t around 0 83.2%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-40}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-24}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 7: 66.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-6}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.85e-6) (- x a) (if (<= z 9.8e-48) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.85e-6) {
		tmp = x - a;
	} else if (z <= 9.8e-48) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.85d-6)) then
        tmp = x - a
    else if (z <= 9.8d-48) then
        tmp = x
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.85e-6) {
		tmp = x - a;
	} else if (z <= 9.8e-48) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.85e-6:
		tmp = x - a
	elif z <= 9.8e-48:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.85e-6)
		tmp = Float64(x - a);
	elseif (z <= 9.8e-48)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.85e-6)
		tmp = x - a;
	elseif (z <= 9.8e-48)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.85e-6], N[(x - a), $MachinePrecision], If[LessEqual[z, 9.8e-48], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8500000000000001e-6 or 9.8000000000000005e-48 < z

   1. Initial program 89.5%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 73.8%

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

   if -1.8500000000000001e-6 < z < 9.8000000000000005e-48

   1. Initial program 99.9%

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

      1. associate-/r/ 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 95.9%

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

      1. associate-/l* 98.2%

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

   6. Simplified 98.2%

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

   7. Taylor expanded in x around inf 64.2%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-6}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 8: 56.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-182}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.6e-198) x (if (<= x 8e-182) (- a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.6e-198) {
		tmp = x;
	} else if (x <= 8e-182) {
		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 <= (-3.6d-198)) then
        tmp = x
    else if (x <= 8d-182) 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 <= -3.6e-198) {
		tmp = x;
	} else if (x <= 8e-182) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.6e-198:
		tmp = x
	elif x <= 8e-182:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.6e-198)
		tmp = x;
	elseif (x <= 8e-182)
		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 <= -3.6e-198)
		tmp = x;
	elseif (x <= 8e-182)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.6e-198], x, If[LessEqual[x, 8e-182], (-a), x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.59999999999999998e-198 or 8.0000000000000004e-182 < x

   1. Initial program 98.4%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 69.8%

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

      1. associate-/l* 71.6%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in x around inf 63.4%

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

   if -3.59999999999999998e-198 < x < 8.0000000000000004e-182

   1. Initial program 75.6%

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

      1. associate-/r/ 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 48.4%

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

      1. mul-1-neg 48.4%

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

      2. *-commutative 48.4%

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

      3. associate--l+ 48.4%

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

      4. +-commutative 48.4%

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

      5. associate-*l/ 54.4%

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

      6. distribute-lft-neg-in 54.4%

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

      7. distribute-neg-frac 54.4%

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

      8. +-commutative 54.4%

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

   6. Simplified 54.4%

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

   7. Taylor expanded in x around 0 37.8%

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

   8. Taylor expanded in z around inf 40.3%

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

      1. mul-1-neg 40.3%

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

   10. Simplified 40.3%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-182}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 54.6% 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 94.2%

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

   1. associate-/r/ 99.9%

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

   2. *-commutative 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in z around 0 65.9%

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

   1. associate-/l* 67.4%

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

6. Simplified 67.4%

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

7. Taylor expanded in x around inf 54.2%

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

8. Final simplification 54.2%

   \[\leadsto x \]

Developer target: 99.8% 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 2023293 
(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))))