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

Percentage Accurate: 97.1% → 99.6%

Time: 10.6s

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

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

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 97.4%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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. Final simplification 99.2%

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

Alternative 2: 75.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z - y}{t}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-135}:\\ \;\;\;\;x + \frac{y}{\frac{z + -1}{a}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+69}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ (- z y) t)))))
   (if (<= t -7.5e-7)
     t_1
     (if (<= t -2e-135)
       (+ x (/ y (/ (+ z -1.0) a)))
       (if (<= t 6.2e+69) (- x (* a (/ z (+ z -1.0)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * ((z - y) / t));
	double tmp;
	if (t <= -7.5e-7) {
		tmp = t_1;
	} else if (t <= -2e-135) {
		tmp = x + (y / ((z + -1.0) / a));
	} else if (t <= 6.2e+69) {
		tmp = x - (a * (z / (z + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a * ((z - y) / t))
    if (t <= (-7.5d-7)) then
        tmp = t_1
    else if (t <= (-2d-135)) then
        tmp = x + (y / ((z + (-1.0d0)) / a))
    else if (t <= 6.2d+69) then
        tmp = x - (a * (z / (z + (-1.0d0))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * ((z - y) / t));
	double tmp;
	if (t <= -7.5e-7) {
		tmp = t_1;
	} else if (t <= -2e-135) {
		tmp = x + (y / ((z + -1.0) / a));
	} else if (t <= 6.2e+69) {
		tmp = x - (a * (z / (z + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * ((z - y) / t))
	tmp = 0
	if t <= -7.5e-7:
		tmp = t_1
	elif t <= -2e-135:
		tmp = x + (y / ((z + -1.0) / a))
	elif t <= 6.2e+69:
		tmp = x - (a * (z / (z + -1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(Float64(z - y) / t)))
	tmp = 0.0
	if (t <= -7.5e-7)
		tmp = t_1;
	elseif (t <= -2e-135)
		tmp = Float64(x + Float64(y / Float64(Float64(z + -1.0) / a)));
	elseif (t <= 6.2e+69)
		tmp = Float64(x - Float64(a * Float64(z / Float64(z + -1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a * ((z - y) / t));
	tmp = 0.0;
	if (t <= -7.5e-7)
		tmp = t_1;
	elseif (t <= -2e-135)
		tmp = x + (y / ((z + -1.0) / a));
	elseif (t <= 6.2e+69)
		tmp = x - (a * (z / (z + -1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e-7], t$95$1, If[LessEqual[t, -2e-135], N[(x + N[(y / N[(N[(z + -1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+69], N[(x - N[(a * N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5000000000000002e-7 or 6.1999999999999997e69 < t

   1. Initial program 99.2%

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

      1. associate-/r/ 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in t around inf 84.4%

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

   if -7.5000000000000002e-7 < t < -2.0000000000000001e-135

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 99.8%

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

   4. Taylor expanded in y around inf 92.5%

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

   if -2.0000000000000001e-135 < t < 6.1999999999999997e69

   1. Initial program 95.5%

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

   3. Taylor expanded in t around 0 91.8%

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

   4. Taylor expanded in y around 0 64.3%

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

      1. mul-1-neg 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in a around 0 64.3%

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

      1. mul-1-neg 64.3%

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

      2. distribute-frac-neg2 64.3%

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

      3. associate-*r/ 78.0%

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

      4. neg-sub0 78.0%

         \[\leadsto x - a \cdot \frac{z}{\color{blue}{0 - \left(1 - z\right)}} \]

      5. associate--r- 78.0%

         \[\leadsto x - a \cdot \frac{z}{\color{blue}{\left(0 - 1\right) + z}} \]

      6. metadata-eval 78.0%

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

   9. Simplified 78.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-7}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-135}:\\ \;\;\;\;x + \frac{y}{\frac{z + -1}{a}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+69}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z - y}{t}\\ \mathbf{if}\;t \leq -4100:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-138}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+70}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ (- z y) t)))))
   (if (<= t -4100.0)
     t_1
     (if (<= t -1.45e-138)
       (- x (* y a))
       (if (<= t 2.15e+70) (- x (* a (/ z (+ z -1.0)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * ((z - y) / t));
	double tmp;
	if (t <= -4100.0) {
		tmp = t_1;
	} else if (t <= -1.45e-138) {
		tmp = x - (y * a);
	} else if (t <= 2.15e+70) {
		tmp = x - (a * (z / (z + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (a * ((z - y) / t))
    if (t <= (-4100.0d0)) then
        tmp = t_1
    else if (t <= (-1.45d-138)) then
        tmp = x - (y * a)
    else if (t <= 2.15d+70) then
        tmp = x - (a * (z / (z + (-1.0d0))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * ((z - y) / t));
	double tmp;
	if (t <= -4100.0) {
		tmp = t_1;
	} else if (t <= -1.45e-138) {
		tmp = x - (y * a);
	} else if (t <= 2.15e+70) {
		tmp = x - (a * (z / (z + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * ((z - y) / t))
	tmp = 0
	if t <= -4100.0:
		tmp = t_1
	elif t <= -1.45e-138:
		tmp = x - (y * a)
	elif t <= 2.15e+70:
		tmp = x - (a * (z / (z + -1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(Float64(z - y) / t)))
	tmp = 0.0
	if (t <= -4100.0)
		tmp = t_1;
	elseif (t <= -1.45e-138)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 2.15e+70)
		tmp = Float64(x - Float64(a * Float64(z / Float64(z + -1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a * ((z - y) / t));
	tmp = 0.0;
	if (t <= -4100.0)
		tmp = t_1;
	elseif (t <= -1.45e-138)
		tmp = x - (y * a);
	elseif (t <= 2.15e+70)
		tmp = x - (a * (z / (z + -1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4100.0], t$95$1, If[LessEqual[t, -1.45e-138], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e+70], N[(x - N[(a * N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4100 or 2.15e70 < t

   1. Initial program 99.2%

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

      1. associate-/r/ 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in t around inf 86.1%

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

   if -4100 < t < -1.44999999999999987e-138

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 99.8%

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

   4. Taylor expanded in z around 0 83.2%

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

   if -1.44999999999999987e-138 < t < 2.15e70

   1. Initial program 95.5%

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

   3. Taylor expanded in t around 0 91.8%

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

   4. Taylor expanded in y around 0 64.3%

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

      1. mul-1-neg 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in a around 0 64.3%

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

      1. mul-1-neg 64.3%

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

      2. distribute-frac-neg2 64.3%

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

      3. associate-*r/ 78.0%

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

      4. neg-sub0 78.0%

         \[\leadsto x - a \cdot \frac{z}{\color{blue}{0 - \left(1 - z\right)}} \]

      5. associate--r- 78.0%

         \[\leadsto x - a \cdot \frac{z}{\color{blue}{\left(0 - 1\right) + z}} \]

      6. metadata-eval 78.0%

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

   9. Simplified 78.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4100:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-138}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+70}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+89} \lor \neg \left(t \leq 5.1 \cdot 10^{+54}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{z + -1}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.8e+89) (not (<= t 5.1e+54)))
   (+ x (* a (/ (- z y) t)))
   (- x (/ (- z y) (/ (+ z -1.0) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e+89) || !(t <= 5.1e+54)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - ((z - y) / ((z + -1.0) / 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 ((t <= (-1.8d+89)) .or. (.not. (t <= 5.1d+54))) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = x - ((z - y) / ((z + (-1.0d0)) / 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 ((t <= -1.8e+89) || !(t <= 5.1e+54)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x - ((z - y) / ((z + -1.0) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.8e+89) or not (t <= 5.1e+54):
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x - ((z - y) / ((z + -1.0) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.8e+89) || !(t <= 5.1e+54))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = Float64(x - Float64(Float64(z - y) / Float64(Float64(z + -1.0) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.8e+89) || ~((t <= 5.1e+54)))
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x - ((z - y) / ((z + -1.0) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.8e+89], N[Not[LessEqual[t, 5.1e+54]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z - y), $MachinePrecision] / N[(N[(z + -1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e89 or 5.10000000000000009e54 < t

   1. Initial program 98.1%

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

      1. associate-/r/ 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around inf 88.6%

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

   if -1.8e89 < t < 5.10000000000000009e54

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0 92.5%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+89} \lor \neg \left(t \leq 5.1 \cdot 10^{+54}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - y}{\frac{z + -1}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+41}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+41)
   (- x a)
   (if (<= z 0.165)
     (+ x (/ (* y a) (- -1.0 t)))
     (- x (* a (/ z (+ z -1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+41) {
		tmp = x - a;
	} else if (z <= 0.165) {
		tmp = x + ((y * a) / (-1.0 - t));
	} else {
		tmp = x - (a * (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 (z <= (-3.5d+41)) then
        tmp = x - a
    else if (z <= 0.165d0) then
        tmp = x + ((y * a) / ((-1.0d0) - t))
    else
        tmp = x - (a * (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 (z <= -3.5e+41) {
		tmp = x - a;
	} else if (z <= 0.165) {
		tmp = x + ((y * a) / (-1.0 - t));
	} else {
		tmp = x - (a * (z / (z + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+41:
		tmp = x - a
	elif z <= 0.165:
		tmp = x + ((y * a) / (-1.0 - t))
	else:
		tmp = x - (a * (z / (z + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+41)
		tmp = Float64(x - a);
	elseif (z <= 0.165)
		tmp = Float64(x + Float64(Float64(y * a) / Float64(-1.0 - t)));
	else
		tmp = Float64(x - Float64(a * Float64(z / Float64(z + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.5e+41)
		tmp = x - a;
	elseif (z <= 0.165)
		tmp = x + ((y * a) / (-1.0 - t));
	else
		tmp = x - (a * (z / (z + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+41], N[(x - a), $MachinePrecision], If[LessEqual[z, 0.165], N[(x + N[(N[(y * a), $MachinePrecision] / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4999999999999999e41

   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%

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

   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 91.4%

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

   if -3.4999999999999999e41 < z < 0.165000000000000008

   1. Initial program 99.8%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around 0 89.5%

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

   if 0.165000000000000008 < z

   1. Initial program 94.8%

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

   3. Taylor expanded in t around 0 77.8%

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

   4. Taylor expanded in y around 0 61.0%

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

      1. mul-1-neg 61.0%

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

   6. Simplified 61.0%

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

   7. Taylor expanded in a around 0 61.0%

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

      1. mul-1-neg 61.0%

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

      2. distribute-frac-neg2 61.0%

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

      3. associate-*r/ 77.4%

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

      4. neg-sub0 77.4%

         \[\leadsto x - a \cdot \frac{z}{\color{blue}{0 - \left(1 - z\right)}} \]

      5. associate--r- 77.4%

         \[\leadsto x - a \cdot \frac{z}{\color{blue}{\left(0 - 1\right) + z}} \]

      6. metadata-eval 77.4%

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

   9. Simplified 77.4%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+41}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 0.165:\\ \;\;\;\;x + \frac{y \cdot a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+42}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.45e+42)
   (- x a)
   (if (<= z 1.15e-16) (- x (* y a)) (- x (* a (/ z (+ z -1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.45e+42) {
		tmp = x - a;
	} else if (z <= 1.15e-16) {
		tmp = x - (y * a);
	} else {
		tmp = x - (a * (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 (z <= (-1.45d+42)) then
        tmp = x - a
    else if (z <= 1.15d-16) then
        tmp = x - (y * a)
    else
        tmp = x - (a * (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 (z <= -1.45e+42) {
		tmp = x - a;
	} else if (z <= 1.15e-16) {
		tmp = x - (y * a);
	} else {
		tmp = x - (a * (z / (z + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.45e+42:
		tmp = x - a
	elif z <= 1.15e-16:
		tmp = x - (y * a)
	else:
		tmp = x - (a * (z / (z + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.45e+42)
		tmp = Float64(x - a);
	elseif (z <= 1.15e-16)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = Float64(x - Float64(a * Float64(z / Float64(z + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.45e+42)
		tmp = x - a;
	elseif (z <= 1.15e-16)
		tmp = x - (y * a);
	else
		tmp = x - (a * (z / (z + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.45e+42], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.15e-16], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(z / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e42

   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%

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

   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 91.4%

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

   if -1.4499999999999999e42 < z < 1.15e-16

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 73.0%

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

   4. Taylor expanded in z around 0 70.8%

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

   if 1.15e-16 < z

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0 77.7%

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

   4. Taylor expanded in y around 0 61.8%

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

      1. mul-1-neg 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in a around 0 61.8%

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

      1. mul-1-neg 61.8%

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

      2. distribute-frac-neg2 61.8%

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

      3. associate-*r/ 77.2%

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

      4. neg-sub0 77.2%

         \[\leadsto x - a \cdot \frac{z}{\color{blue}{0 - \left(1 - z\right)}} \]

      5. associate--r- 77.2%

         \[\leadsto x - a \cdot \frac{z}{\color{blue}{\left(0 - 1\right) + z}} \]

      6. metadata-eval 77.2%

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

   9. Simplified 77.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+42}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{z}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+41} \lor \neg \left(z \leq 1.35 \cdot 10^{-16}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.4e+41) (not (<= z 1.35e-16))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e+41) || !(z <= 1.35e-16)) {
		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 <= (-2.4d+41)) .or. (.not. (z <= 1.35d-16))) 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 <= -2.4e+41) || !(z <= 1.35e-16)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.4e+41) or not (z <= 1.35e-16):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.4e+41) || !(z <= 1.35e-16))
		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 <= -2.4e+41) || ~((z <= 1.35e-16)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.4e+41], N[Not[LessEqual[z, 1.35e-16]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000002e41 or 1.35e-16 < z

   1. Initial program 94.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 82.6%

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

   if -2.4000000000000002e41 < z < 1.35e-16

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 73.0%

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

   4. Taylor expanded in z around 0 70.8%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+41} \lor \neg \left(z \leq 1.35 \cdot 10^{-16}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+41} \lor \neg \left(z \leq 8.2 \cdot 10^{-20}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.4e+41) (not (<= z 8.2e-20))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e+41) || !(z <= 8.2e-20)) {
		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 <= (-2.4d+41)) .or. (.not. (z <= 8.2d-20))) 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 <= -2.4e+41) || !(z <= 8.2e-20)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.4e+41) or not (z <= 8.2e-20):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.4e+41) || !(z <= 8.2e-20))
		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 <= -2.4e+41) || ~((z <= 8.2e-20)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.4e+41], N[Not[LessEqual[z, 8.2e-20]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000002e41 or 8.2000000000000002e-20 < z

   1. Initial program 95.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 82.0%

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

   if -2.4000000000000002e41 < z < 8.2000000000000002e-20

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-/r/ 98.5%

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

      4. distribute-rgt-neg-in 98.5%

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

      5. associate-*l/ 97.0%

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

      6. associate-/l* 99.9%

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

      7. fma-define 99.9%

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

      8. distribute-frac-neg 99.9%

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

      9. distribute-neg-frac2 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. sub-neg 99.9%

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

      12. distribute-neg-in 99.9%

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

      13. remove-double-neg 99.9%

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

      14. +-commutative 99.9%

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

      15. sub-neg 99.9%

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

      16. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 54.6%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+41} \lor \neg \left(z \leq 8.2 \cdot 10^{-20}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+120} \lor \neg \left(a \leq 10^{+48}\right):\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.6e+120) (not (<= a 1e+48))) (- a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.6e+120) || !(a <= 1e+48)) {
		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 <= (-1.6d+120)) .or. (.not. (a <= 1d+48))) 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 <= -1.6e+120) || !(a <= 1e+48)) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.6e+120) or not (a <= 1e+48):
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.6e+120) || !(a <= 1e+48))
		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 <= -1.6e+120) || ~((a <= 1e+48)))
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.6e+120], N[Not[LessEqual[a, 1e+48]], $MachinePrecision]], (-a), x]

Derivation

1. Split input into 2 regimes

2. if a < -1.59999999999999991e120 or 1.00000000000000004e48 < a

   1. Initial program 99.8%

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

      1. associate-/r/ 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around inf 41.8%

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

   6. Taylor expanded in x around 0 34.8%

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

      1. neg-mul-1 34.8%

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

   8. Simplified 34.8%

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

   if -1.59999999999999991e120 < a < 1.00000000000000004e48

   1. Initial program 96.0%

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

      1. sub-neg 96.0%

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

      2. +-commutative 96.0%

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

      3. associate-/r/ 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. associate-*l/ 99.9%

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

      6. associate-/l* 96.3%

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

      7. fma-define 96.3%

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

      8. distribute-frac-neg 96.3%

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

      9. distribute-neg-frac2 96.3%

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

      10. distribute-neg-in 96.3%

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

      11. sub-neg 96.3%

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

      12. distribute-neg-in 96.3%

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

      13. remove-double-neg 96.3%

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

      14. +-commutative 96.3%

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

      15. sub-neg 96.3%

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

      16. metadata-eval 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in a around 0 70.1%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+120} \lor \neg \left(a \leq 10^{+48}\right):\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.1% 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 97.4%

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

   1. sub-neg 97.4%

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

   2. +-commutative 97.4%

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

   3. associate-/r/ 99.2%

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

   4. distribute-rgt-neg-in 99.2%

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

   5. associate-*l/ 86.4%

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

   6. associate-/l* 97.6%

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

   7. fma-define 97.6%

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

   8. distribute-frac-neg 97.6%

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

   9. distribute-neg-frac2 97.6%

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

   10. distribute-neg-in 97.6%

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

   11. sub-neg 97.6%

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

   12. distribute-neg-in 97.6%

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

   13. remove-double-neg 97.6%

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

   14. +-commutative 97.6%

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

   15. sub-neg 97.6%

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

   16. metadata-eval 97.6%

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

3. Simplified 97.6%

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

5. Taylor expanded in a around 0 51.2%

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

Developer Target 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024165 
(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))))