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

Percentage Accurate: 97.0% → 99.6%

Time: 11.2s

Alternatives: 12

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: 99.6% 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]

Derivation

1. Initial program 97.3%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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. Final simplification 99.9%

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

Alternative 2: 74.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(z - y\right)\\ t_2 := x - a \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+21}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-225}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (- z y)))) (t_2 (- x (* a (/ y t)))))
   (if (<= z -9.5e+21)
     (- x a)
     (if (<= z -1.55e-36)
       t_2
       (if (<= z 3.7e-250)
         t_1
         (if (<= z 1.75e-225) t_2 (if (<= z 1.08e-7) t_1 (- x a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z - y));
	double t_2 = x - (a * (y / t));
	double tmp;
	if (z <= -9.5e+21) {
		tmp = x - a;
	} else if (z <= -1.55e-36) {
		tmp = t_2;
	} else if (z <= 3.7e-250) {
		tmp = t_1;
	} else if (z <= 1.75e-225) {
		tmp = t_2;
	} else if (z <= 1.08e-7) {
		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) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (z - y))
    t_2 = x - (a * (y / t))
    if (z <= (-9.5d+21)) then
        tmp = x - a
    else if (z <= (-1.55d-36)) then
        tmp = t_2
    else if (z <= 3.7d-250) then
        tmp = t_1
    else if (z <= 1.75d-225) then
        tmp = t_2
    else if (z <= 1.08d-7) 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 + (a * (z - y));
	double t_2 = x - (a * (y / t));
	double tmp;
	if (z <= -9.5e+21) {
		tmp = x - a;
	} else if (z <= -1.55e-36) {
		tmp = t_2;
	} else if (z <= 3.7e-250) {
		tmp = t_1;
	} else if (z <= 1.75e-225) {
		tmp = t_2;
	} else if (z <= 1.08e-7) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * (z - y))
	t_2 = x - (a * (y / t))
	tmp = 0
	if z <= -9.5e+21:
		tmp = x - a
	elif z <= -1.55e-36:
		tmp = t_2
	elif z <= 3.7e-250:
		tmp = t_1
	elif z <= 1.75e-225:
		tmp = t_2
	elif z <= 1.08e-7:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(z - y)))
	t_2 = Float64(x - Float64(a * Float64(y / t)))
	tmp = 0.0
	if (z <= -9.5e+21)
		tmp = Float64(x - a);
	elseif (z <= -1.55e-36)
		tmp = t_2;
	elseif (z <= 3.7e-250)
		tmp = t_1;
	elseif (z <= 1.75e-225)
		tmp = t_2;
	elseif (z <= 1.08e-7)
		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 + (a * (z - y));
	t_2 = x - (a * (y / t));
	tmp = 0.0;
	if (z <= -9.5e+21)
		tmp = x - a;
	elseif (z <= -1.55e-36)
		tmp = t_2;
	elseif (z <= 3.7e-250)
		tmp = t_1;
	elseif (z <= 1.75e-225)
		tmp = t_2;
	elseif (z <= 1.08e-7)
		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[(a * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+21], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.55e-36], t$95$2, If[LessEqual[z, 3.7e-250], t$95$1, If[LessEqual[z, 1.75e-225], t$95$2, If[LessEqual[z, 1.08e-7], t$95$1, N[(x - a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.500000000000001e21 or 1.08000000000000001e-7 < z

   1. Initial program 94.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 76.1%

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

   if -9.500000000000001e21 < z < -1.5499999999999999e-36 or 3.6999999999999998e-250 < z < 1.7499999999999999e-225

   1. Initial program 99.8%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 93.8%

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

   6. Taylor expanded in y around inf 88.9%

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

   if -1.5499999999999999e-36 < z < 3.6999999999999998e-250 or 1.7499999999999999e-225 < z < 1.08000000000000001e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.2%

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

   4. Taylor expanded in t around 0 77.1%

      \[\leadsto x - \color{blue}{a \cdot \left(y - z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+21}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-36}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-250}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-225}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-7}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(z - y\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+25}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-26}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-225}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (- z y)))))
   (if (<= z -3.8e+25)
     (- x a)
     (if (<= z -4.1e-26)
       (- x (/ y (/ t a)))
       (if (<= z 1.75e-255)
         t_1
         (if (<= z 3.2e-225)
           (- x (* a (/ y t)))
           (if (<= z 1.08e-7) t_1 (- x a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z - y));
	double tmp;
	if (z <= -3.8e+25) {
		tmp = x - a;
	} else if (z <= -4.1e-26) {
		tmp = x - (y / (t / a));
	} else if (z <= 1.75e-255) {
		tmp = t_1;
	} else if (z <= 3.2e-225) {
		tmp = x - (a * (y / t));
	} else if (z <= 1.08e-7) {
		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 + (a * (z - y))
    if (z <= (-3.8d+25)) then
        tmp = x - a
    else if (z <= (-4.1d-26)) then
        tmp = x - (y / (t / a))
    else if (z <= 1.75d-255) then
        tmp = t_1
    else if (z <= 3.2d-225) then
        tmp = x - (a * (y / t))
    else if (z <= 1.08d-7) 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 + (a * (z - y));
	double tmp;
	if (z <= -3.8e+25) {
		tmp = x - a;
	} else if (z <= -4.1e-26) {
		tmp = x - (y / (t / a));
	} else if (z <= 1.75e-255) {
		tmp = t_1;
	} else if (z <= 3.2e-225) {
		tmp = x - (a * (y / t));
	} else if (z <= 1.08e-7) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * (z - y))
	tmp = 0
	if z <= -3.8e+25:
		tmp = x - a
	elif z <= -4.1e-26:
		tmp = x - (y / (t / a))
	elif z <= 1.75e-255:
		tmp = t_1
	elif z <= 3.2e-225:
		tmp = x - (a * (y / t))
	elif z <= 1.08e-7:
		tmp = t_1
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(z - y)))
	tmp = 0.0
	if (z <= -3.8e+25)
		tmp = Float64(x - a);
	elseif (z <= -4.1e-26)
		tmp = Float64(x - Float64(y / Float64(t / a)));
	elseif (z <= 1.75e-255)
		tmp = t_1;
	elseif (z <= 3.2e-225)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (z <= 1.08e-7)
		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 + (a * (z - y));
	tmp = 0.0;
	if (z <= -3.8e+25)
		tmp = x - a;
	elseif (z <= -4.1e-26)
		tmp = x - (y / (t / a));
	elseif (z <= 1.75e-255)
		tmp = t_1;
	elseif (z <= 3.2e-225)
		tmp = x - (a * (y / t));
	elseif (z <= 1.08e-7)
		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[(a * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+25], N[(x - a), $MachinePrecision], If[LessEqual[z, -4.1e-26], N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-255], t$95$1, If[LessEqual[z, 3.2e-225], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e-7], t$95$1, N[(x - a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.8e25 or 1.08000000000000001e-7 < z

   1. Initial program 94.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 76.1%

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

   if -3.8e25 < z < -4.0999999999999999e-26

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 t around inf 89.7%

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

   6. Taylor expanded in y around inf 81.5%

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

      1. associate-*l/ 73.9%

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

      2. associate-/l* 81.6%

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

   8. Applied egg-rr 81.6%

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

   if -4.0999999999999999e-26 < z < 1.74999999999999989e-255 or 3.19999999999999975e-225 < z < 1.08000000000000001e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.2%

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

   4. Taylor expanded in t around 0 77.1%

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

   if 1.74999999999999989e-255 < z < 3.19999999999999975e-225

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 inf 100.0%

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

   6. Taylor expanded in y around inf 100.0%

      \[\leadsto x - \color{blue}{\frac{y}{t}} \cdot a \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+25}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-26}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-255}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-225}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-7}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{-61} \lor \neg \left(z \leq 2.6 \cdot 10^{-8}\right):\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.7e-61) (not (<= z 2.6e-8)))
   (+ 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 <= -5.7e-61) || !(z <= 2.6e-8)) {
		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 <= (-5.7d-61)) .or. (.not. (z <= 2.6d-8))) 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 <= -5.7e-61) || !(z <= 2.6e-8)) {
		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 <= -5.7e-61) or not (z <= 2.6e-8):
		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 <= -5.7e-61) || !(z <= 2.6e-8))
		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 <= -5.7e-61) || ~((z <= 2.6e-8)))
		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, -5.7e-61], N[Not[LessEqual[z, 2.6e-8]], $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 < -5.70000000000000005e-61 or 2.6000000000000001e-8 < z

   1. Initial program 95.5%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 95.5%

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

      2. div-inv 95.4%

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

      3. associate-/r* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0 64.8%

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

      1. sub-neg 64.8%

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

      2. mul-1-neg 64.8%

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

      3. remove-double-neg 64.8%

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

      4. associate-/l* 83.6%

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

      5. associate--l+ 83.6%

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

   9. Simplified 83.6%

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

   if -5.70000000000000005e-61 < z < 2.6000000000000001e-8

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   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 0 94.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{-61} \lor \neg \left(z \leq 2.6 \cdot 10^{-8}\right):\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+23} \lor \neg \left(z \leq 3.5 \cdot 10^{-8}\right):\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{t + 1}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.4e+23) (not (<= z 3.5e-8)))
   (+ x (/ a (/ (+ (- t z) 1.0) z)))
   (+ x (/ (- z y) (/ (+ t 1.0) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e+23) || !(z <= 3.5e-8)) {
		tmp = x + (a / (((t - z) + 1.0) / z));
	} else {
		tmp = x + ((z - y) / ((t + 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 ((z <= (-2.4d+23)) .or. (.not. (z <= 3.5d-8))) then
        tmp = x + (a / (((t - z) + 1.0d0) / z))
    else
        tmp = x + ((z - y) / ((t + 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 ((z <= -2.4e+23) || !(z <= 3.5e-8)) {
		tmp = x + (a / (((t - z) + 1.0) / z));
	} else {
		tmp = x + ((z - y) / ((t + 1.0) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.4e+23) or not (z <= 3.5e-8):
		tmp = x + (a / (((t - z) + 1.0) / z))
	else:
		tmp = x + ((z - y) / ((t + 1.0) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.4e+23) || !(z <= 3.5e-8))
		tmp = Float64(x + Float64(a / Float64(Float64(Float64(t - z) + 1.0) / z)));
	else
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(t + 1.0) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.4e+23) || ~((z <= 3.5e-8)))
		tmp = x + (a / (((t - z) + 1.0) / z));
	else
		tmp = x + ((z - y) / ((t + 1.0) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.4e+23], N[Not[LessEqual[z, 3.5e-8]], $MachinePrecision]], N[(x + N[(a / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - y), $MachinePrecision] / N[(N[(t + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e23 or 3.50000000000000024e-8 < 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. Step-by-step derivation

      1. associate-/r/ 94.9%

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

      2. div-inv 94.8%

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

      3. associate-/r* 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 63.4%

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

      1. sub-neg 63.4%

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

      2. mul-1-neg 63.4%

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

      3. remove-double-neg 63.4%

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

      4. associate-/l* 84.9%

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

      5. associate--l+ 84.9%

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

   9. Simplified 84.9%

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

   if -2.4e23 < z < 3.50000000000000024e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 98.6%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+23} \lor \neg \left(z \leq 3.5 \cdot 10^{-8}\right):\\ \;\;\;\;x + \frac{a}{\frac{\left(t - z\right) + 1}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{t + 1}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+21} \lor \neg \left(z \leq 3.5 \cdot 10^{-8}\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{t + 1}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.6e+21) (not (<= z 3.5e-8)))
   (+ x (* a (/ z (+ (- t z) 1.0))))
   (+ x (/ (- z y) (/ (+ t 1.0) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.6e+21) || !(z <= 3.5e-8)) {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	} else {
		tmp = x + ((z - y) / ((t + 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 ((z <= (-4.6d+21)) .or. (.not. (z <= 3.5d-8))) then
        tmp = x + (a * (z / ((t - z) + 1.0d0)))
    else
        tmp = x + ((z - y) / ((t + 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 ((z <= -4.6e+21) || !(z <= 3.5e-8)) {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	} else {
		tmp = x + ((z - y) / ((t + 1.0) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.6e+21) or not (z <= 3.5e-8):
		tmp = x + (a * (z / ((t - z) + 1.0)))
	else:
		tmp = x + ((z - y) / ((t + 1.0) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.6e+21) || !(z <= 3.5e-8))
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(t - z) + 1.0))));
	else
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(t + 1.0) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.6e+21) || ~((z <= 3.5e-8)))
		tmp = x + (a * (z / ((t - z) + 1.0)));
	else
		tmp = x + ((z - y) / ((t + 1.0) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.6e+21], N[Not[LessEqual[z, 3.5e-8]], $MachinePrecision]], N[(x + N[(a * N[(z / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - y), $MachinePrecision] / N[(N[(t + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6e21 or 3.50000000000000024e-8 < 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 y around 0 84.9%

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

      1. associate-*r/ 84.9%

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

      2. neg-mul-1 84.9%

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

      3. associate--l+ 84.9%

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

   7. Simplified 84.9%

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

   if -4.6e21 < z < 3.50000000000000024e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 98.6%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+21} \lor \neg \left(z \leq 3.5 \cdot 10^{-8}\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{t + 1}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+27} \lor \neg \left(z \leq 9 \cdot 10^{+31}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.8e+27) (not (<= z 9e+31)))
   (+ x (/ (- z y) (/ (- z) a)))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.8e+27) || !(z <= 9e+31)) {
		tmp = x + ((z - y) / (-z / 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 <= (-1.8d+27)) .or. (.not. (z <= 9d+31))) then
        tmp = x + ((z - y) / (-z / 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 <= -1.8e+27) || !(z <= 9e+31)) {
		tmp = x + ((z - y) / (-z / a));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.8e+27) or not (z <= 9e+31):
		tmp = x + ((z - y) / (-z / a))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.8e+27) || !(z <= 9e+31))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(-z) / 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 <= -1.8e+27) || ~((z <= 9e+31)))
		tmp = x + ((z - y) / (-z / 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, -1.8e+27], N[Not[LessEqual[z, 9e+31]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[((-z) / a), $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 < -1.79999999999999991e27 or 8.9999999999999992e31 < z

   1. Initial program 94.6%

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

   3. Taylor expanded in z around inf 81.9%

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

      1. mul-1-neg 81.9%

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

      2. distribute-neg-frac 81.9%

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

   5. Simplified 81.9%

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

   if -1.79999999999999991e27 < z < 8.9999999999999992e31

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   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 0 88.7%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+27} \lor \neg \left(z \leq 9 \cdot 10^{+31}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+27} \lor \neg \left(z \leq 9.5 \cdot 10^{+114}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+27) (not (<= z 9.5e+114)))
   (- 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 <= -1.45e+27) || !(z <= 9.5e+114)) {
		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 <= (-1.45d+27)) .or. (.not. (z <= 9.5d+114))) 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 <= -1.45e+27) || !(z <= 9.5e+114)) {
		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 <= -1.45e+27) or not (z <= 9.5e+114):
		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 <= -1.45e+27) || !(z <= 9.5e+114))
		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 <= -1.45e+27) || ~((z <= 9.5e+114)))
		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, -1.45e+27], N[Not[LessEqual[z, 9.5e+114]], $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 < -1.4500000000000001e27 or 9.5000000000000001e114 < z

   1. Initial program 93.6%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 81.9%

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

   if -1.4500000000000001e27 < z < 9.5000000000000001e114

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   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 0 85.0%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+27} \lor \neg \left(z \leq 9.5 \cdot 10^{+114}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+20} \lor \neg \left(z \leq 1.08 \cdot 10^{-7}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e+20) (not (<= z 1.08e-7))) (- x a) (+ x (* a (- z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+20) || !(z <= 1.08e-7)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.5d+20)) .or. (.not. (z <= 1.08d-7))) then
        tmp = x - a
    else
        tmp = x + (a * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+20) || !(z <= 1.08e-7)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.5e+20) or not (z <= 1.08e-7):
		tmp = x - a
	else:
		tmp = x + (a * (z - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e+20) || !(z <= 1.08e-7))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.5e+20) || ~((z <= 1.08e-7)))
		tmp = x - a;
	else
		tmp = x + (a * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e+20], N[Not[LessEqual[z, 1.08e-7]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e20 or 1.08000000000000001e-7 < z

   1. Initial program 94.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 76.1%

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

   if -3.5e20 < z < 1.08000000000000001e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 98.4%

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

   4. Taylor expanded in t around 0 70.8%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+20} \lor \neg \left(z \leq 1.08 \cdot 10^{-7}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+21} \lor \neg \left(z \leq 1.08 \cdot 10^{-7}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.02e+21) (not (<= z 1.08e-7))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.02e+21) || !(z <= 1.08e-7)) {
		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 <= (-1.02d+21)) .or. (.not. (z <= 1.08d-7))) 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 <= -1.02e+21) || !(z <= 1.08e-7)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.02e+21) or not (z <= 1.08e-7):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.02e+21) || !(z <= 1.08e-7))
		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 <= -1.02e+21) || ~((z <= 1.08e-7)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.02e+21], N[Not[LessEqual[z, 1.08e-7]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e21 or 1.08000000000000001e-7 < z

   1. Initial program 94.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 76.1%

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

   if -1.02e21 < z < 1.08000000000000001e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 72.1%

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

   4. Taylor expanded in z around 0 67.5%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+21} \lor \neg \left(z \leq 1.08 \cdot 10^{-7}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+28} \lor \neg \left(z \leq 1.08 \cdot 10^{-7}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.55e+28) (not (<= z 1.08e-7))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e+28) || !(z <= 1.08e-7)) {
		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 <= (-1.55d+28)) .or. (.not. (z <= 1.08d-7))) 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 <= -1.55e+28) || !(z <= 1.08e-7)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.55e+28) or not (z <= 1.08e-7):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.55e+28) || !(z <= 1.08e-7))
		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 <= -1.55e+28) || ~((z <= 1.08e-7)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.55e+28], N[Not[LessEqual[z, 1.08e-7]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e28 or 1.08000000000000001e-7 < z

   1. Initial program 94.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 75.9%

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

   if -1.55e28 < z < 1.08000000000000001e-7

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 55.2%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+28} \lor \neg \left(z \leq 1.08 \cdot 10^{-7}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.0% 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 97.3%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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 x around inf 48.9%

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

6. Final simplification 48.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024031 
(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))))