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

Percentage Accurate: 96.9% → 99.5%

Time: 11.1s

Alternatives: 13

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: 96.9% 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: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / (((t - z) + 1.0d0) / (z - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

   1. associate-/r/ 99.5%

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

3. Simplified 99.5%

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

   1. *-commutative 99.5%

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

   2. clear-num 99.5%

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

   3. un-div-inv 99.5%

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

6. Applied egg-rr 99.5%

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

7. Final simplification 99.5%

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

Alternative 2: 70.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-181}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(1 - \frac{a}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.0)
   (- x (* a (/ y t)))
   (if (<= t 2.5e-181)
     (- x (* a y))
     (if (<= t 5.8e-13) (* x (- 1.0 (/ a x))) (- x (/ y (/ t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.0) {
		tmp = x - (a * (y / t));
	} else if (t <= 2.5e-181) {
		tmp = x - (a * y);
	} else if (t <= 5.8e-13) {
		tmp = x * (1.0 - (a / x));
	} else {
		tmp = x - (y / (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.0d0)) then
        tmp = x - (a * (y / t))
    else if (t <= 2.5d-181) then
        tmp = x - (a * y)
    else if (t <= 5.8d-13) then
        tmp = x * (1.0d0 - (a / x))
    else
        tmp = x - (y / (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.0) {
		tmp = x - (a * (y / t));
	} else if (t <= 2.5e-181) {
		tmp = x - (a * y);
	} else if (t <= 5.8e-13) {
		tmp = x * (1.0 - (a / x));
	} else {
		tmp = x - (y / (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.0:
		tmp = x - (a * (y / t))
	elif t <= 2.5e-181:
		tmp = x - (a * y)
	elif t <= 5.8e-13:
		tmp = x * (1.0 - (a / x))
	else:
		tmp = x - (y / (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.0)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (t <= 2.5e-181)
		tmp = Float64(x - Float64(a * y));
	elseif (t <= 5.8e-13)
		tmp = Float64(x * Float64(1.0 - Float64(a / x)));
	else
		tmp = Float64(x - Float64(y / Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.0)
		tmp = x - (a * (y / t));
	elseif (t <= 2.5e-181)
		tmp = x - (a * y);
	elseif (t <= 5.8e-13)
		tmp = x * (1.0 - (a / x));
	else
		tmp = x - (y / (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.0], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-181], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-13], N[(x * N[(1.0 - N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1

   1. Initial program 96.2%

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

      1. associate-/r/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around inf 80.9%

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

   6. Taylor expanded in y around inf 73.7%

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

      1. associate-/l* 77.8%

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

   8. Simplified 77.8%

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

   if -1 < t < 2.5000000000000001e-181

   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 t around 0 99.9%

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

   6. Taylor expanded in z around 0 71.7%

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

   if 2.5000000000000001e-181 < t < 5.7999999999999995e-13

   1. Initial program 97.5%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 76.0%

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

   6. Taylor expanded in x around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. unsub-neg 78.3%

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

   8. Simplified 78.3%

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

   if 5.7999999999999995e-13 < t

   1. Initial program 97.5%

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

   3. Taylor expanded in t around inf 85.7%

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

   4. Taylor expanded in y around inf 85.6%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-181}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(1 - \frac{a}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -0.96:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-181}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 0.0014:\\ \;\;\;\;x \cdot \left(1 - \frac{a}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y t)))))
   (if (<= t -0.96)
     t_1
     (if (<= t 2.2e-181)
       (- x (* a y))
       (if (<= t 0.0014) (* x (- 1.0 (/ a x))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / t));
	double tmp;
	if (t <= -0.96) {
		tmp = t_1;
	} else if (t <= 2.2e-181) {
		tmp = x - (a * y);
	} else if (t <= 0.0014) {
		tmp = x * (1.0 - (a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (a * (y / t))
    if (t <= (-0.96d0)) then
        tmp = t_1
    else if (t <= 2.2d-181) then
        tmp = x - (a * y)
    else if (t <= 0.0014d0) then
        tmp = x * (1.0d0 - (a / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / t));
	double tmp;
	if (t <= -0.96) {
		tmp = t_1;
	} else if (t <= 2.2e-181) {
		tmp = x - (a * y);
	} else if (t <= 0.0014) {
		tmp = x * (1.0 - (a / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (y / t))
	tmp = 0
	if t <= -0.96:
		tmp = t_1
	elif t <= 2.2e-181:
		tmp = x - (a * y)
	elif t <= 0.0014:
		tmp = x * (1.0 - (a / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / t)))
	tmp = 0.0
	if (t <= -0.96)
		tmp = t_1;
	elseif (t <= 2.2e-181)
		tmp = Float64(x - Float64(a * y));
	elseif (t <= 0.0014)
		tmp = Float64(x * Float64(1.0 - Float64(a / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (y / t));
	tmp = 0.0;
	if (t <= -0.96)
		tmp = t_1;
	elseif (t <= 2.2e-181)
		tmp = x - (a * y);
	elseif (t <= 0.0014)
		tmp = x * (1.0 - (a / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.96], t$95$1, If[LessEqual[t, 2.2e-181], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.0014], N[(x * N[(1.0 - N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.95999999999999996 or 0.00139999999999999999 < t

   1. Initial program 96.8%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around inf 78.7%

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

   6. Taylor expanded in y around inf 75.5%

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

      1. associate-/l* 81.6%

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

   8. Simplified 81.6%

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

   if -0.95999999999999996 < t < 2.19999999999999997e-181

   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 t around 0 99.9%

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

   6. Taylor expanded in z around 0 71.7%

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

   if 2.19999999999999997e-181 < t < 0.00139999999999999999

   1. Initial program 97.5%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 76.0%

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

   6. Taylor expanded in x around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. unsub-neg 78.3%

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

   8. Simplified 78.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{a}{x}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.96:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-181}:\\ \;\;\;\;x - a \cdot y\\ \mathbf{elif}\;t \leq 0.0014:\\ \;\;\;\;x \cdot \left(1 - \frac{a}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -20 \lor \neg \left(t \leq 3.2 \cdot 10^{+115}\right):\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -20.0) (not (<= t 3.2e+115)))
   (- x (/ (- y z) (/ t a)))
   (+ x (* a (/ (- y z) (+ z -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -20.0) || !(t <= 3.2e+115)) {
		tmp = x - ((y - z) / (t / a));
	} else {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-20.0d0)) .or. (.not. (t <= 3.2d+115))) then
        tmp = x - ((y - z) / (t / a))
    else
        tmp = x + (a * ((y - z) / (z + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -20.0) || !(t <= 3.2e+115)) {
		tmp = x - ((y - z) / (t / a));
	} else {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -20.0) or not (t <= 3.2e+115):
		tmp = x - ((y - z) / (t / a))
	else:
		tmp = x + (a * ((y - z) / (z + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -20.0) || !(t <= 3.2e+115))
		tmp = Float64(x - Float64(Float64(y - z) / Float64(t / a)));
	else
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / Float64(z + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -20.0) || ~((t <= 3.2e+115)))
		tmp = x - ((y - z) / (t / a));
	else
		tmp = x + (a * ((y - z) / (z + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -20.0], N[Not[LessEqual[t, 3.2e+115]], $MachinePrecision]], N[(x - N[(N[(y - z), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -20 or 3.2e115 < t

   1. Initial program 97.0%

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

   3. Taylor expanded in t around inf 87.3%

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

   if -20 < t < 3.2e115

   1. Initial program 97.2%

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

      1. associate-/r/ 99.9%

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

   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 t around 0 97.4%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -20 \lor \neg \left(t \leq 3.2 \cdot 10^{+115}\right):\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05:\\ \;\;\;\;x - \frac{y - z}{\frac{t + 1}{a}}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+109}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.05)
   (- x (/ (- y z) (/ (+ t 1.0) a)))
   (if (<= t 7.2e+109)
     (+ x (* a (/ (- y z) (+ z -1.0))))
     (- x (/ (- y z) (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05) {
		tmp = x - ((y - z) / ((t + 1.0) / a));
	} else if (t <= 7.2e+109) {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	} else {
		tmp = x - ((y - z) / (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.05d0)) then
        tmp = x - ((y - z) / ((t + 1.0d0) / a))
    else if (t <= 7.2d+109) then
        tmp = x + (a * ((y - z) / (z + (-1.0d0))))
    else
        tmp = x - ((y - z) / (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05) {
		tmp = x - ((y - z) / ((t + 1.0) / a));
	} else if (t <= 7.2e+109) {
		tmp = x + (a * ((y - z) / (z + -1.0)));
	} else {
		tmp = x - ((y - z) / (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.05:
		tmp = x - ((y - z) / ((t + 1.0) / a))
	elif t <= 7.2e+109:
		tmp = x + (a * ((y - z) / (z + -1.0)))
	else:
		tmp = x - ((y - z) / (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.05)
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(t + 1.0) / a)));
	elseif (t <= 7.2e+109)
		tmp = Float64(x + Float64(a * Float64(Float64(y - z) / Float64(z + -1.0))));
	else
		tmp = Float64(x - Float64(Float64(y - z) / Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.05)
		tmp = x - ((y - z) / ((t + 1.0) / a));
	elseif (t <= 7.2e+109)
		tmp = x + (a * ((y - z) / (z + -1.0)));
	else
		tmp = x - ((y - z) / (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.05], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(t + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+109], N[(x + N[(a * N[(N[(y - z), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05000000000000004

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0 85.6%

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

   if -1.05000000000000004 < t < 7.2e109

   1. Initial program 97.2%

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

      1. associate-/r/ 99.9%

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

   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 t around 0 97.4%

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

   if 7.2e109 < t

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf 92.6%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05:\\ \;\;\;\;x - \frac{y - z}{\frac{t + 1}{a}}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+109}:\\ \;\;\;\;x + a \cdot \frac{y - z}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+48} \lor \neg \left(z \leq 0.0016\right):\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e+48) (not (<= z 0.0016)))
   (+ x (/ (- y z) (/ z a)))
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+48) || !(z <= 0.0016)) {
		tmp = x + ((y - z) / (z / a));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.5d+48)) .or. (.not. (z <= 0.0016d0))) then
        tmp = x + ((y - z) / (z / a))
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+48) || !(z <= 0.0016)) {
		tmp = x + ((y - z) / (z / a));
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.5e+48) or not (z <= 0.0016):
		tmp = x + ((y - z) / (z / a))
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e+48) || !(z <= 0.0016))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.5e+48) || ~((z <= 0.0016)))
		tmp = x + ((y - z) / (z / a));
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e+48], N[Not[LessEqual[z, 0.0016]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4999999999999997e48 or 0.00160000000000000008 < z

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf 84.7%

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

      1. associate-*r/ 84.7%

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

      2. neg-mul-1 84.7%

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

   5. Simplified 84.7%

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

   if -3.4999999999999997e48 < z < 0.00160000000000000008

   1. Initial program 98.6%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 90.7%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+48} \lor \neg \left(z \leq 0.0016\right):\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+48} \lor \neg \left(z \leq 1.12 \cdot 10^{+18}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.4e+48) (not (<= z 1.12e+18)))
   (- x a)
   (+ x (* a (/ y (- -1.0 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e+48) || !(z <= 1.12e+18)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.4d+48)) .or. (.not. (z <= 1.12d+18))) then
        tmp = x - a
    else
        tmp = x + (a * (y / ((-1.0d0) - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e+48) || !(z <= 1.12e+18)) {
		tmp = x - a;
	} else {
		tmp = x + (a * (y / (-1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.4e+48) or not (z <= 1.12e+18):
		tmp = x - a
	else:
		tmp = x + (a * (y / (-1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.4e+48) || !(z <= 1.12e+18))
		tmp = Float64(x - a);
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.4e+48) || ~((z <= 1.12e+18)))
		tmp = x - a;
	else
		tmp = x + (a * (y / (-1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.4e+48], N[Not[LessEqual[z, 1.12e+18]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4000000000000001e48 or 1.12e18 < z

   1. Initial program 95.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 79.3%

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

   if -2.4000000000000001e48 < z < 1.12e18

   1. Initial program 98.7%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 90.4%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+48} \lor \neg \left(z \leq 1.12 \cdot 10^{+18}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+41}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{elif}\;z \leq 0.0016:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+41)
   (+ x (* a (/ z (+ (- t z) 1.0))))
   (if (<= z 0.0016) (+ x (* a (/ y (- -1.0 t)))) (+ x (/ (- y z) (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+41) {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	} else if (z <= 0.0016) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + ((y - z) / (z / 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 <= (-1d+41)) then
        tmp = x + (a * (z / ((t - z) + 1.0d0)))
    else if (z <= 0.0016d0) then
        tmp = x + (a * (y / ((-1.0d0) - t)))
    else
        tmp = x + ((y - z) / (z / 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 <= -1e+41) {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	} else if (z <= 0.0016) {
		tmp = x + (a * (y / (-1.0 - t)));
	} else {
		tmp = x + ((y - z) / (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+41:
		tmp = x + (a * (z / ((t - z) + 1.0)))
	elif z <= 0.0016:
		tmp = x + (a * (y / (-1.0 - t)))
	else:
		tmp = x + ((y - z) / (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+41)
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(t - z) + 1.0))));
	elseif (z <= 0.0016)
		tmp = Float64(x + Float64(a * Float64(y / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e+41)
		tmp = x + (a * (z / ((t - z) + 1.0)));
	elseif (z <= 0.0016)
		tmp = x + (a * (y / (-1.0 - t)));
	else
		tmp = x + ((y - z) / (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+41], N[(x + N[(a * N[(z / N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0016], N[(x + N[(a * N[(y / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.00000000000000001e41

   1. Initial program 89.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 88.7%

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

      1. associate--l+ 88.7%

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

      2. +-commutative 88.7%

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

      3. neg-mul-1 88.7%

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

      4. distribute-neg-frac2 88.7%

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

      5. +-commutative 88.7%

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

      6. distribute-neg-in 88.7%

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

      7. metadata-eval 88.7%

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

      8. unsub-neg 88.7%

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

   7. Simplified 88.7%

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

   if -1.00000000000000001e41 < z < 0.00160000000000000008

   1. Initial program 99.1%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 91.2%

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

   if 0.00160000000000000008 < z

   1. Initial program 97.4%

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

   3. Taylor expanded in z around inf 87.3%

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

      1. associate-*r/ 87.3%

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

      2. neg-mul-1 87.3%

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

   5. Simplified 87.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+41}:\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{elif}\;z \leq 0.0016:\\ \;\;\;\;x + a \cdot \frac{y}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{z}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+47} \lor \neg \left(z \leq 7.4 \cdot 10^{-20}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e+47) (not (<= z 7.4e-20))) (- x a) (- x (* a y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+47) || !(z <= 7.4e-20)) {
		tmp = x - a;
	} else {
		tmp = x - (a * 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 <= (-1.1d+47)) .or. (.not. (z <= 7.4d-20))) then
        tmp = x - a
    else
        tmp = x - (a * 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 <= -1.1e+47) || !(z <= 7.4e-20)) {
		tmp = x - a;
	} else {
		tmp = x - (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e+47) or not (z <= 7.4e-20):
		tmp = x - a
	else:
		tmp = x - (a * y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e+47) || !(z <= 7.4e-20))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.1e+47) || ~((z <= 7.4e-20)))
		tmp = x - a;
	else
		tmp = x - (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.1e+47], N[Not[LessEqual[z, 7.4e-20]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e47 or 7.4000000000000001e-20 < z

   1. Initial program 95.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 z around inf 78.2%

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

   if -1.1e47 < z < 7.4000000000000001e-20

   1. Initial program 98.6%

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

      1. associate-/r/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around 0 73.2%

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

   6. Taylor expanded in z around 0 69.2%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+47} \lor \neg \left(z \leq 7.4 \cdot 10^{-20}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+50} \lor \neg \left(z \leq 13000000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+50) (not (<= z 13000000000.0))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+50) || !(z <= 13000000000.0)) {
		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 <= (-9.5d+50)) .or. (.not. (z <= 13000000000.0d0))) 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 <= -9.5e+50) || !(z <= 13000000000.0)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e+50) or not (z <= 13000000000.0):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+50) || !(z <= 13000000000.0))
		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 <= -9.5e+50) || ~((z <= 13000000000.0)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+50], N[Not[LessEqual[z, 13000000000.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999993e50 or 1.3e10 < z

   1. Initial program 95.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 78.6%

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

   if -9.4999999999999993e50 < z < 1.3e10

   1. Initial program 98.7%

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

      1. associate-/r/ 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around inf 44.9%

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

   6. Taylor expanded in x around inf 54.8%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+50} \lor \neg \left(z \leq 13000000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

   1. associate-/r/ 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 12: 55.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 8.6 \cdot 10^{+189}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 8.6e+189) x (- a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 8.6e+189) {
		tmp = x;
	} else {
		tmp = -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 (a <= 8.6d+189) then
        tmp = x
    else
        tmp = -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 (a <= 8.6e+189) {
		tmp = x;
	} else {
		tmp = -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 8.6e+189:
		tmp = x
	else:
		tmp = -a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 8.6e+189)
		tmp = x;
	else
		tmp = Float64(-a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 8.6e+189)
		tmp = x;
	else
		tmp = -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 8.6e+189], x, (-a)]

Derivation

1. Split input into 2 regimes

2. if a < 8.59999999999999995e189

   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. Add Preprocessing

   5. Taylor expanded in z around inf 62.9%

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

   6. Taylor expanded in x around inf 61.2%

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

   if 8.59999999999999995e189 < a

   1. Initial program 99.8%

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

      1. associate-/r/ 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in z around inf 29.7%

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

   6. Taylor expanded in x around 0 24.1%

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

      1. mul-1-neg 24.1%

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

   8. Simplified 24.1%

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

Alternative 13: 54.1% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

   1. associate-/r/ 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in z around inf 59.5%

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

6. Taylor expanded in x around inf 55.6%

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

Developer Target 1: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024139 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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