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

Percentage Accurate: 97.2% → 99.6%

Time: 9.2s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.2% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.8%

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

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

Alternative 2: 70.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot a\\ t_2 := x - a \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-131}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-306}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 55000000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y a))) (t_2 (- x (* a (/ y t)))))
   (if (<= t -1.35e+34)
     t_2
     (if (<= t -2.5e-131)
       (- x a)
       (if (<= t -2.6e-264)
         t_1
         (if (<= t -6.5e-306)
           (- x a)
           (if (<= t 55000000000000.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double t_2 = x - (a * (y / t));
	double tmp;
	if (t <= -1.35e+34) {
		tmp = t_2;
	} else if (t <= -2.5e-131) {
		tmp = x - a;
	} else if (t <= -2.6e-264) {
		tmp = t_1;
	} else if (t <= -6.5e-306) {
		tmp = x - a;
	} else if (t <= 55000000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 - (y * a)
    t_2 = x - (a * (y / t))
    if (t <= (-1.35d+34)) then
        tmp = t_2
    else if (t <= (-2.5d-131)) then
        tmp = x - a
    else if (t <= (-2.6d-264)) then
        tmp = t_1
    else if (t <= (-6.5d-306)) then
        tmp = x - a
    else if (t <= 55000000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * a);
	double t_2 = x - (a * (y / t));
	double tmp;
	if (t <= -1.35e+34) {
		tmp = t_2;
	} else if (t <= -2.5e-131) {
		tmp = x - a;
	} else if (t <= -2.6e-264) {
		tmp = t_1;
	} else if (t <= -6.5e-306) {
		tmp = x - a;
	} else if (t <= 55000000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * a)
	t_2 = x - (a * (y / t))
	tmp = 0
	if t <= -1.35e+34:
		tmp = t_2
	elif t <= -2.5e-131:
		tmp = x - a
	elif t <= -2.6e-264:
		tmp = t_1
	elif t <= -6.5e-306:
		tmp = x - a
	elif t <= 55000000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * a))
	t_2 = Float64(x - Float64(a * Float64(y / t)))
	tmp = 0.0
	if (t <= -1.35e+34)
		tmp = t_2;
	elseif (t <= -2.5e-131)
		tmp = Float64(x - a);
	elseif (t <= -2.6e-264)
		tmp = t_1;
	elseif (t <= -6.5e-306)
		tmp = Float64(x - a);
	elseif (t <= 55000000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * a);
	t_2 = x - (a * (y / t));
	tmp = 0.0;
	if (t <= -1.35e+34)
		tmp = t_2;
	elseif (t <= -2.5e-131)
		tmp = x - a;
	elseif (t <= -2.6e-264)
		tmp = t_1;
	elseif (t <= -6.5e-306)
		tmp = x - a;
	elseif (t <= 55000000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+34], t$95$2, If[LessEqual[t, -2.5e-131], N[(x - a), $MachinePrecision], If[LessEqual[t, -2.6e-264], t$95$1, If[LessEqual[t, -6.5e-306], N[(x - a), $MachinePrecision], If[LessEqual[t, 55000000000000.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35e34 or 5.5e13 < t

   1. Initial program 94.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around inf 88.4%

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

   5. Taylor expanded in y around inf 76.0%

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

      1. associate-/l* 79.9%

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

      2. associate-/r/ 83.1%

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

   7. Simplified 83.1%

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

   if -1.35e34 < t < -2.5000000000000002e-131 or -2.6000000000000002e-264 < t < -6.5000000000000004e-306

   1. Initial program 95.9%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 75.4%

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

   if -2.5000000000000002e-131 < t < -2.6000000000000002e-264 or -6.5000000000000004e-306 < t < 5.5e13

   1. Initial program 97.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around 0 100.0%

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

   5. Taylor expanded in z around 0 77.5%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+34}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-131}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-264}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-306}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 55000000000000:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]

Alternative 3: 72.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{a}{\frac{1 - z}{z}}\\ t_2 := x - a \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.45 \cdot 10^{-107}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ a (/ (- 1.0 z) z)))) (t_2 (- x (* a (/ y t)))))
   (if (<= t -1.1e+34)
     t_2
     (if (<= t 4.9e-254)
       t_1
       (if (<= t 4.45e-107) (- x (* y a)) (if (<= t 3.4e+24) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a / ((1.0 - z) / z));
	double t_2 = x - (a * (y / t));
	double tmp;
	if (t <= -1.1e+34) {
		tmp = t_2;
	} else if (t <= 4.9e-254) {
		tmp = t_1;
	} else if (t <= 4.45e-107) {
		tmp = x - (y * a);
	} else if (t <= 3.4e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 / ((1.0d0 - z) / z))
    t_2 = x - (a * (y / t))
    if (t <= (-1.1d+34)) then
        tmp = t_2
    else if (t <= 4.9d-254) then
        tmp = t_1
    else if (t <= 4.45d-107) then
        tmp = x - (y * a)
    else if (t <= 3.4d+24) then
        tmp = t_1
    else
        tmp = t_2
    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 / ((1.0 - z) / z));
	double t_2 = x - (a * (y / t));
	double tmp;
	if (t <= -1.1e+34) {
		tmp = t_2;
	} else if (t <= 4.9e-254) {
		tmp = t_1;
	} else if (t <= 4.45e-107) {
		tmp = x - (y * a);
	} else if (t <= 3.4e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a / ((1.0 - z) / z))
	t_2 = x - (a * (y / t))
	tmp = 0
	if t <= -1.1e+34:
		tmp = t_2
	elif t <= 4.9e-254:
		tmp = t_1
	elif t <= 4.45e-107:
		tmp = x - (y * a)
	elif t <= 3.4e+24:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a / Float64(Float64(1.0 - z) / z)))
	t_2 = Float64(x - Float64(a * Float64(y / t)))
	tmp = 0.0
	if (t <= -1.1e+34)
		tmp = t_2;
	elseif (t <= 4.9e-254)
		tmp = t_1;
	elseif (t <= 4.45e-107)
		tmp = Float64(x - Float64(y * a));
	elseif (t <= 3.4e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a / ((1.0 - z) / z));
	t_2 = x - (a * (y / t));
	tmp = 0.0;
	if (t <= -1.1e+34)
		tmp = t_2;
	elseif (t <= 4.9e-254)
		tmp = t_1;
	elseif (t <= 4.45e-107)
		tmp = x - (y * a);
	elseif (t <= 3.4e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a / N[(N[(1.0 - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+34], t$95$2, If[LessEqual[t, 4.9e-254], t$95$1, If[LessEqual[t, 4.45e-107], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+24], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1000000000000001e34 or 3.4000000000000001e24 < t

   1. Initial program 94.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 88.2%

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

   5. Taylor expanded in y around inf 76.4%

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

      1. associate-/l* 80.3%

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

      2. associate-/r/ 83.6%

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

   7. Simplified 83.6%

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

   if -1.1000000000000001e34 < t < 4.8999999999999998e-254 or 4.4500000000000002e-107 < t < 3.4000000000000001e24

   1. Initial program 98.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around 0 97.5%

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

   5. Taylor expanded in y around 0 73.5%

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

      1. sub-neg 73.5%

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

      2. mul-1-neg 73.5%

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

      3. remove-double-neg 73.5%

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

      4. associate-/l* 80.4%

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

   7. Simplified 80.4%

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

   if 4.8999999999999998e-254 < t < 4.4500000000000002e-107

   1. Initial program 93.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 99.9%

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

   5. Taylor expanded in z around 0 76.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-254}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{elif}\;t \leq 4.45 \cdot 10^{-107}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 91.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+34} \lor \neg \left(t \leq 6.5 \cdot 10^{+17}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e+34) (not (<= t 6.5e+17)))
   (+ x (* a (/ (- z y) t)))
   (+ x (* a (/ (- z y) (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e+34) || !(t <= 6.5e+17)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.3d+34)) .or. (.not. (t <= 6.5d+17))) then
        tmp = x + (a * ((z - y) / t))
    else
        tmp = x + (a * ((z - y) / (1.0d0 - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e+34) || !(t <= 6.5e+17)) {
		tmp = x + (a * ((z - y) / t));
	} else {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.3e+34) or not (t <= 6.5e+17):
		tmp = x + (a * ((z - y) / t))
	else:
		tmp = x + (a * ((z - y) / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.3e+34) || !(t <= 6.5e+17))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / t)));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.3e+34) || ~((t <= 6.5e+17)))
		tmp = x + (a * ((z - y) / t));
	else
		tmp = x + (a * ((z - y) / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.3e+34], N[Not[LessEqual[t, 6.5e+17]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.29999999999999999e34 or 6.5e17 < t

   1. Initial program 94.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around inf 88.4%

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

   if -1.29999999999999999e34 < t < 6.5e17

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around 0 99.2%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+34} \lor \neg \left(t \leq 6.5 \cdot 10^{+17}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \end{array} \]

Alternative 5: 91.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-9} \lor \neg \left(z \leq 2.3 \cdot 10^{-15}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{t + 1}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e-9) (not (<= z 2.3e-15)))
   (+ x (* a (/ (- z y) (- 1.0 z))))
   (- x (/ (- y z) (/ (+ t 1.0) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e-9) || !(z <= 2.3e-15)) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else {
		tmp = x - ((y - z) / ((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 <= (-1.65d-9)) .or. (.not. (z <= 2.3d-15))) then
        tmp = x + (a * ((z - y) / (1.0d0 - z)))
    else
        tmp = x - ((y - z) / ((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 <= -1.65e-9) || !(z <= 2.3e-15)) {
		tmp = x + (a * ((z - y) / (1.0 - z)));
	} else {
		tmp = x - ((y - z) / ((t + 1.0) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e-9) or not (z <= 2.3e-15):
		tmp = x + (a * ((z - y) / (1.0 - z)))
	else:
		tmp = x - ((y - z) / ((t + 1.0) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e-9) || !(z <= 2.3e-15))
		tmp = Float64(x + Float64(a * Float64(Float64(z - y) / Float64(1.0 - z))));
	else
		tmp = Float64(x - Float64(Float64(y - z) / 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 <= -1.65e-9) || ~((z <= 2.3e-15)))
		tmp = x + (a * ((z - y) / (1.0 - z)));
	else
		tmp = x - ((y - z) / ((t + 1.0) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e-9], N[Not[LessEqual[z, 2.3e-15]], $MachinePrecision]], N[(x + N[(a * N[(N[(z - y), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(t + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65000000000000009e-9 or 2.2999999999999999e-15 < 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. Taylor expanded in t around 0 91.5%

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

   if -1.65000000000000009e-9 < z < 2.2999999999999999e-15

   1. Initial program 96.9%

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

   2. Taylor expanded in z around 0 96.9%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-9} \lor \neg \left(z \leq 2.3 \cdot 10^{-15}\right):\\ \;\;\;\;x + a \cdot \frac{z - y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{t + 1}{a}}\\ \end{array} \]

Alternative 6: 86.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-9} \lor \neg \left(z \leq 2.3 \cdot 10^{-15}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e-9) (not (<= z 2.3e-15)))
   (+ 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 <= -1.65e-9) || !(z <= 2.3e-15)) {
		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 <= (-1.65d-9)) .or. (.not. (z <= 2.3d-15))) 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 <= -1.65e-9) || !(z <= 2.3e-15)) {
		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 <= -1.65e-9) or not (z <= 2.3e-15):
		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 <= -1.65e-9) || !(z <= 2.3e-15))
		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 <= -1.65e-9) || ~((z <= 2.3e-15)))
		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, -1.65e-9], N[Not[LessEqual[z, 2.3e-15]], $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 < -1.65000000000000009e-9 or 2.2999999999999999e-15 < z

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 85.3%

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

      1. mul-1-neg 85.3%

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

      2. distribute-neg-frac 85.3%

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

   4. Simplified 85.3%

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

   if -1.65000000000000009e-9 < z < 2.2999999999999999e-15

   1. Initial program 96.9%

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

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-9} \lor \neg \left(z \leq 2.3 \cdot 10^{-15}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]

Alternative 7: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+84}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-15}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e+84)
   (- x a)
   (if (<= z 2.3e-15)
     (- x (* a (/ y (+ t 1.0))))
     (+ x (/ a (/ (- 1.0 z) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e+84) {
		tmp = x - a;
	} else if (z <= 2.3e-15) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = x + (a / ((1.0 - z) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.6d+84)) then
        tmp = x - a
    else if (z <= 2.3d-15) then
        tmp = x - (a * (y / (t + 1.0d0)))
    else
        tmp = x + (a / ((1.0d0 - z) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e+84) {
		tmp = x - a;
	} else if (z <= 2.3e-15) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = x + (a / ((1.0 - z) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e+84:
		tmp = x - a
	elif z <= 2.3e-15:
		tmp = x - (a * (y / (t + 1.0)))
	else:
		tmp = x + (a / ((1.0 - z) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e+84)
		tmp = Float64(x - a);
	elseif (z <= 2.3e-15)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	else
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 - z) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.6e+84)
		tmp = x - a;
	elseif (z <= 2.3e-15)
		tmp = x - (a * (y / (t + 1.0)));
	else
		tmp = x + (a / ((1.0 - z) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e+84], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.3e-15], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a / N[(N[(1.0 - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000005e84

   1. Initial program 94.0%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 89.4%

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

   if -1.60000000000000005e84 < z < 2.2999999999999999e-15

   1. Initial program 96.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around 0 89.7%

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

   if 2.2999999999999999e-15 < z

   1. Initial program 95.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 92.3%

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

   5. Taylor expanded in y around 0 72.2%

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

      1. sub-neg 72.2%

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

      2. mul-1-neg 72.2%

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

      3. remove-double-neg 72.2%

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

      4. associate-/l* 84.5%

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

   7. Simplified 84.5%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+84}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-15}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \end{array} \]

Alternative 8: 65.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -60000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-33}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -60000.0) (- x a) (if (<= z 2e-33) (+ x (* z a)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -60000.0) {
		tmp = x - a;
	} else if (z <= 2e-33) {
		tmp = x + (z * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-60000.0d0)) then
        tmp = x - a
    else if (z <= 2d-33) then
        tmp = x + (z * a)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -60000.0) {
		tmp = x - a;
	} else if (z <= 2e-33) {
		tmp = x + (z * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -60000.0:
		tmp = x - a
	elif z <= 2e-33:
		tmp = x + (z * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -60000.0)
		tmp = Float64(x - a);
	elseif (z <= 2e-33)
		tmp = Float64(x + Float64(z * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -60000.0)
		tmp = x - a;
	elseif (z <= 2e-33)
		tmp = x + (z * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -60000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 2e-33], N[(x + N[(z * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6e4 or 2.0000000000000001e-33 < 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. Taylor expanded in z around inf 81.4%

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

   if -6e4 < z < 2.0000000000000001e-33

   1. Initial program 96.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around 0 70.7%

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

   5. Taylor expanded in y around 0 55.1%

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

      1. associate-*r/ 55.1%

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

      2. associate-*r* 55.1%

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

      3. mul-1-neg 55.1%

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

   7. Simplified 55.1%

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

   8. Taylor expanded in z around 0 54.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -60000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-33}:\\ \;\;\;\;x + z \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 9: 72.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-20}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-33}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e-20) (- x a) (if (<= z 2.8e-33) (- x (* y a)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e-20) {
		tmp = x - a;
	} else if (z <= 2.8e-33) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.2d-20)) then
        tmp = x - a
    else if (z <= 2.8d-33) then
        tmp = x - (y * a)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e-20) {
		tmp = x - a;
	} else if (z <= 2.8e-33) {
		tmp = x - (y * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e-20:
		tmp = x - a
	elif z <= 2.8e-33:
		tmp = x - (y * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e-20)
		tmp = Float64(x - a);
	elseif (z <= 2.8e-33)
		tmp = Float64(x - Float64(y * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e-20)
		tmp = x - a;
	elseif (z <= 2.8e-33)
		tmp = x - (y * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e-20], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.8e-33], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.1999999999999999e-20 or 2.8e-33 < z

   1. Initial program 94.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 79.8%

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

   if -5.1999999999999999e-20 < z < 2.8e-33

   1. Initial program 97.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in t around 0 71.6%

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

   5. Taylor expanded in z around 0 68.7%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-20}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-33}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 10: 64.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+80}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+80) (- x a) (if (<= z 2.25e-33) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+80) {
		tmp = x - a;
	} else if (z <= 2.25e-33) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.5d+80)) then
        tmp = x - a
    else if (z <= 2.25d-33) then
        tmp = x
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+80) {
		tmp = x - a;
	} else if (z <= 2.25e-33) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+80:
		tmp = x - a
	elif z <= 2.25e-33:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+80)
		tmp = Float64(x - a);
	elseif (z <= 2.25e-33)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e+80)
		tmp = x - a;
	elseif (z <= 2.25e-33)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+80], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.25e-33], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4999999999999998e80 or 2.24999999999999995e-33 < 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. Taylor expanded in z around inf 84.9%

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

   if -6.4999999999999998e80 < z < 2.24999999999999995e-33

   1. Initial program 96.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in x around inf 54.8%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+80}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 11: 53.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 95.8%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
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. Taylor expanded in x around inf 56.3%

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

5. Final simplification 56.3%

   \[\leadsto x \]

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 2023176 
(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))))